Search

This paper explores time-varying black holes within the framework of the Einstein-Gauss-Bonnet theory with two scalar fields, examining the propagation of gravitational waves (GW). In reconstructed models, ghosts frequently emerge but can be eliminated by applying certain constraints. We investigate the behavior of high-frequency gravitational waves by examining the effects of varying Gauss-Bonnet coupling during their propagation. The speed of transmission is altered by the coupling in the creation of black holes. The speed of gravitational waves varies as they enter a black hole compared to when they exit.

Physically based changes to general relativity (GR) often predict significant differences in how spacetime behaves near massive neutron stars. One of these modifications is represented by $f(\mathcal{Q}, { \mathcal{T}})$, with $\mathcal{Q}$ being the non-metricity and ${ \mathit{T}}$ representing the energy-momentum tensor trace. This theory is viewed as a neutral expansion of GR. Neutron stars weighing more than 1.8 times the mass of the Sun, when observed as radio pulsars, provide valuable opportunities to test fundamental physics under extreme conditions that are rare in the observable universe and cannot be replicated in experiments conducted on land. We derive an exact solution through utilizing the form $f(\mathcal{Q}, { \mathcal{T}})=\mathcal{Q}+\psi { \mathcal{T}}$, where $\psi$ represents a dimensional expression. We elucidate that all physical quantities within the star can be expressed using the dimensional parameter $\psi$ and the compactness, which is defined as $C=\frac{ 2GM}{Rc^2}$. We set $\psi$ to a maximum value of $\psi_1=\frac{\psi}{\kappa^2}=-0.04$ in the negative range, based on observational constraints related to radius and mass of the pulsar ${\textit SAX J1748.9-2021}$. Here, ${\mathrm \kappa^2}$ represents the coupling constant of Einstein, defined as ${\mathrm \kappa^2=\frac{8\pi G}{c^4}}$. Unlike in GR, the solution we derived results in a stable compact object without violating the conjectured sound speed condition $c_s^2\leq\frac{c^2}3$.It is crucial to mention that no equations of state were assumed in this investigation. Nevertheless, our model fits nicely with linear form. Generally, when $\psi$ is negative, the theory predicts a star with a slightly larger size than GR for the same mass. The difference in predicted size between the theory with a negative $\psi$ and GR for the same mass is attributed to an additional force., Comment: 16 pages and 7 figures will appear in EPJC

In the course of this research, we employ the Gauss-Bonnet equation of motion alongside the scalar field and potential to acquire a fresh solution for a spherically symmetrical charged black hole. Specifically, we derive this black hole solution by employing a metric potential where the components are equal, that is, $g_{tt}=g_{rr}$. In our research, we achieve several accomplishments, including fixing the characteristics of the scalar field, and the Gauss-Bonnet term. We thoroughly examine the physical properties associated with such black hole and show that we have supplementary terms when compared to the Reissner-Nordstr\"om black hole solution. These additional terms are of the order $O(\frac{1}{r^6})$ and $O(\frac{1}{r^9})$. The presence of these supplementary terms can be attributed to the impact of the scalar function denoted as $\xi$. Such expressions play a crucial role in generating the multi-horizon black hole solution. The presence of these extra terms facilitates the derivation of a modified first law of thermodynamics and the corresponding Smarr relation., Comment: 18 pages, 4 figures

We revisit slow rotating black hole (BH) solutions in Chern-Simons modified gravity (CSMG) by considering perturbative solution about Schwarzschild BH. In particular, the case when nondynamical CSMG with noncanonical CS scalar is considered. We provide a new solution different from the previously obtained one \cite{Konno:2007ze} which we refer to as KMT model. The present solution accounts for frame dragging effect which includes not only radial dependence as in the KMT. Nevertheless, it reduces to KMT as a particular case. We show that the tidal gravitational force (Kretschmann invariant) associated to the present solution contains a term of order $1/r^3$ additional to Schwarzschild but absent from directional divergence, unlike KMT model which diverges along the axis of symmetry. We derive the corresponding circular velocity of a massive test particle in which the KMT velocity is recovered in addition to an extra term $\propto r$. We investigate possible constraints on KMT and the present solutions from the observed rotation curve of UGC11455 galaxy as an example. We show that perturbation solutions cannot physically explain the flattening of galactic rotation curves., Comment: 13 pages, 2 figures, match the version that will appear in Phys. Lett. B

The objective of this research is to explore compact celestial objects while considering the framework of an extended gravitational theory known as $\mathcal{R}+f(\mathcal{G})$ gravity. The notations $\mathcal{R}$ and $\mathcal{G}$ denote the Ricci scalar and the Gauss-Bonnet invariant, respectively. Radio pulsars, which are neutron stars with masses greater than 1.8 times that of the Sun ($M_\odot$), provide exceptional opportunities for delving into fundamental physics in extraordinary environments unparalleled in the observable universe and surpassing the capabilities of experiments conducted on Earth. Through the utilization of both the linear and quadratic expressions of the function { $f(\mathcal{G}) = \alpha_1 \mathcal{G}^2$, where $\alpha_1$ (with dimensional units of [${\textit length}^6$]) are incorporated}, we have achieved an accurate analytical solution for anisotropic perfect-fluid spheres in a state of hydrostatic equilibrium. By integrating the dimensional parameters $\alpha_1$ and the compactness factor, defined as ${\mathcal C=\frac{2GM}{Rc^2}}$, we showcase our capacity to encompass and depict all physical characteristics within the stellar structure. We illustrate that the model is capable of producing a stable arrangement encompassing its physical and geometric properties. We illustrate that by utilizing the quadratic form of $\mathcal{G}$ in the $\mathcal{R}+f(\mathcal{G})$ framework, the ansatz of Krori-Barua establishes connection between pressure in the radial direction ($p_r$) using semi-analytical methods, pressure in the tangential direction ($p_t$), and density ($\rho$)., Comment: 19 pages 9 Figures

We discuss spherically symmetric dynamical systems in the framework of a general model of $f({\cal R})$ gravity, i.e. $f({\cal R})={\cal R}e^{\zeta {\cal R}}$, where $\zeta$ is a dimensional quantity in squared length units [L$^2$]. We initially assume that the internal structure of such systems is governed by the Krori-Barua ansatz, alongside the presence of fluid anisotropy. By employing astrophysical observations obtained from the pulsar {\textit SAX J1748.9-2021}, derived from bursting X-ray binaries located within globular clusters, we determine that $\zeta$ is approximately equal to $\pm 5$ km$^2$. In particular, the model can create a stable configuration for {\textit SAX J1748.9-2021}, encompassing its geometric and physical characteristics. In $f({\cal R})$ gravity, the Krori-Barua approach links $p_r$ and $p_t$, which represent the components of the pressures, to ($\rho$), representing the density, semi-analytically. These relations are described as $p_r\approx v_r^2 (\rho-\rho_{I})$ and $p_t\approx v_t^2 (\rho-\rho_{II})$. Here, the expression $v_r$ and $v_t$ represent the radial and tangential sound speeds, respectively. Meanwhile, $\rho_I$ pertains to the surface density and $\rho_{II}$ is derived using the parameters of the model. Notably, within the frame of $f({\cal R})$ gravity where $\zeta$ is negative, the maximum compactness, denoted as $C$, is inherently limited to values that do not exceed the Buchdahl limit. This contrasts with general relativity or with $f({\cal R})$ with positive $\zeta$, where $C$ has the potential to reach the limit of the black hole asymptotically. The predictions of such model suggest a central energy density which largely exceeds the saturation of nuclear density, which has the value $\rho_{\text{nuc}} = 3\times 10^{14}$ g/cm$^3$. Also, the density at the surface $\rho_I$ surpasses $\rho_{\text{nuc}}$., Comment: 28 pages, 8 figures, Will appear in EPJC

In this paper, we investigate the gravitational collapse to form the black hole in the acceleratingly expanding universe in the frame of Einstein--Gauss-Bonnet theory having two scalar fields and we study the propagation of the gravitational wave (GW). This may describe the creation of the primordial black holes in the early stages of the universe and the impact of their creation on the propagation of primordial gravitational waves. The collapsing spacetime can be obtained by using the formulation of the ``reconstruction'', that is, we find a model that realises the desired or given geometry. In the reconstructed models, ghosts often appear, which could be eliminated by imposing constraints. We show that the standard cosmological solutions or self-gravitating objects such as a planet, the Sun, various types of stars, etc., in Einstein's gravity, are also solutions in this model. Using the dynamical value of the Gauss-Bonnet coupling, the propagation of the high-frequency GW is investigated. The propagating speed changes due to the coupling during the period of the black hole formation. The speed of the GW propagation going into the black hole is different from that of the wave going out., Comment: 24 pages, no figure, the title is changed, the version to appear in Physical Review D

This study looks into regular solutions in a theory of gravity called $f(R)$ gravity, which also involves a scalar field. The $f(R)$ theory changes Einstein's ideas by adding a new function related to something called the Ricci scalar. This lets us tweak the equations that describe how gravity works. Adding a scalar field makes the theory more interesting, giving us more ways to investigate and understand it. { The main goal of this research is to create regular black holes using a combination of $f(R)$ gravitational theory and a scalar field.} Regular solutions don't have any singularities, which are points where certain physical quantities, like invariants, become really big or undefined. { In this context, we find two regular black hole solutions by using a spherical space with either an equal or unequal approach.} For the solutions where we use the equal approach, we figure out the shape of $f(R)$ and how it changes, along with its first and second derivatives. We demonstrate that Hayward's solution in this theory stays steady because all the shapes of $f(R)$ and their first and second derivatives are positive. Next, we focus on the case where the metric isn't equal and figure out the black hole solution. We also find out what $f(R)$ and the scalar field look like in this situation. We demonstrate that the solution in this case is a broader version of the Hayward solution. When certain conditions are met, we end up back at the scenario where the metrics are equal. We also prove that this model is stable because $f(R)$, along with its first and second derivatives, are all positive. { We analyze the trajectories of these black hole solutions and determine the forms of their conserved quantities that remain same along those trajectories., Comment: 23 pages, four figures

In this paper, we propose a model including four scalar fields coupled with general gravity theories, which is a generalization of the two-scalar model proposed in Phys. Rev. D \textbf{103} (2021) no.4, 044055, where it has been shown that any given spherically symmetric static/time-dependent spacetime can be realized by using the two-scalar model. We show that by using the four-scalar model, we can construct a model that realizes any given spacetime as a solution even if the spacetime does not have a spherical symmetry or any other symmetry. We also show that by imposing constraints on the scalar fields by using the Lagrange multiplier fields, the scalar fields become non-dynamical and they do not propagate. This tells that there does not appear any sound which is usually generated by the density fluctuation of the fluid. In this sense, the model with the constraints is a most general extension of the mimetic theory in JHEP \textbf{11} (2013), 135, where there appears an effective dark matter. The dark matter is non-dynamical and it does not collapse even under gravitational force. Our model can be regarded as a general extension of any kind of fluid besides dark matter. We may consider the case that the potential of the scalar fields vanishes and the model becomes a non-linear $\sigma$ model. Then our formulation gives a mapping from the geometry of the spacetime to the geometry of the target space of the non-linear $\sigma$ model via gravity theory although the physical meaning has not been clear. We also consider the application of the model to $f(Q)$ gravity theory, which is based on a non-metricity tensor and $Q$ is a scalar quantity constructed from the non-metricity tensor. ..., Comment: LaTeX 12 pages, version to appear in Physics of the Dark Universe

Due to the absence of spherically symmetric black hole solutions in $f(\mathbb{Q})$ because of the constraint derived from its field equations, which yields either $\mathbb{Q}=0 $ or $f_{\mathbb{Q} \mathbb{Q}}=0 $ \cite{Heisenberg:2023lru,Maurya:2023muz}. We are going to introduce a tours solutions for charged anti-de-Sitter black holes in $N$-dimensions within the framework of the quadratic form of $f(\mathbb{Q})$ gravity, where the coincident gauge condition is applied \cite{Heisenberg:2023lru}. Here, $f(\mathbb{Q})=\mathbb{Q}+\frac{1}2\alpha \mathbb{Q}^2-2\Lambda$, and the condition $N \geq 4$ is satisfied. These black hole solutions exhibit flat or cylindrical horizons as their distinctive features. An intriguing aspect of these black hole solutions lies in the coexistence of electric monopole and quadrupole components within the potential field, which are indivisible and exhibit interconnected momenta. This sets them apart from the majority of known charged solutions in the linear form of the non-metricity theory and its extensions. Moreover, the curvature singularities in these solutions are less severe compared to those found in known charged black hole solutions within the characteristic can be demonstrated by computing certain invariants of the curvature and non-metricity tensors. Finally, we calculate thermodynamic parameters, including entropy, Hawking temperature, and Gibbs free energy. These thermodynamic computations affirm the stability of our model., Comment: 13 pages, 3 figures

Solutions pertaining to a Kerr black hole with a flat horizon undergoing gradual rotation are explored in the context of gravitational theories modified by dynamical Chern-Simons terms with cylindrical metrics, which approach asymptotically the anti de Sitter spacetime. It is shown that the cross-term of a metric component is unaffected by the perturbations of the Chern-Simons scalar independently of whether the dynamical Chern-Simons field equation is uncharged or charged with an electric field. From this result, it is ensured that the Chern-Simons scalar field can affect the spaces of the metric that approach asymptotically the flat spacetime only., Comment: 10 pages

We propose a class of models, in which stable gravastar with large surface redshift becomes a solution. In recent decades, gravastars have become a plausible substitute for black holes. Researchers have explored stable gravastar models in various alternative gravity theories, in addition to the conventional framework of general relativity. In this paper, we present a stellar model within the framework of Einstein's gravity with two scalar fields, in accordance with the conjecture proposed by Mazur and Mottola [Proc. Nat. Acad. Sci. \textbf{101} (2004), 9545-9550]. In the model, the two scalar fields become non-dynamical by imposing constraints in order to avoid ghosts. The gravastar comprises two distinct regions, namely: (a) the interior region and (b) the exterior region. We assume the interior region consists of the de Sitter spacetime, and the exterior region is the Schwarzschild one. The two regions are connected with each other by the shell region. On the shell, we assume that the metric is given by a polynomial function of the radial coordinate $r$. The function has six constants. These constants are fixed by the smooth junction conditions, i.e., the interior region with the interior layer of the shell and the exterior region with the exterior layer of the shell. From these boundary conditions, we are able to write the coefficients of the scalar fields in terms of the interior radius and exterior radius. To clarify the philosophy of this study, we also give two examples of spacetimes that asymptote as the de Sitter spacetime for small $r$ and as the Schwarzschild spacetime for large $r$. Exploration is focused on the physical attribute of the shell region, specifically, its proper length., Comment: 18 pages, 8 Figures, will appear in JCAP

In this paper, we construct models that admit the traversable wormhole geometries in the framework of Einstein's gravity with two scalar fields. As well known, the energy conditions are broken and we show that there appears a ghost. The ghost can be, however, eliminated by imposing a constraint on the ghost field, which is a scalar. The constraint is similar to the mimetic one proposed by Chamseddine and Mukhanov to construct an alternative description of cold dark matter. We explicitly show that there does not appear any unstable mode although the energy conditions are broken. Therefore we obtain a model that realizes the traversable and stable wormhole., Comment: 11 pages, one figure

We derive a novel class of four-dimensional black hole solutions in Gauss-Bonnet gravity coupled with a scalar field in presence of Maxwell electrodynamics. In order to derive such solutions, we assume the ansatz $ g_{tt}\neq g_{rr}{}^{-1}$ for metric potentials. Due to the ansatz for the metric, the Reissner Nordstr\"om gauge potential cannot be recovered because of the presence of higher-order terms ${\cal O}\left(\frac{1}{r}\right)$ which are not allowed to be vanishing. Moreover, the scalar field is not allowed to vanish. If it vanishes, a function of the solution results undefined. For this reason, the solution cannot be reduced to a Reissner Nordstr\"om space-time in any limit. Furthermore, it is possible to show that the electric field is of higher-order in the monopole expansion: this fact explicitly comes from the contribution of the scalar field. Therefore, we can conclude that the Gauss-Bonnet scalar field acts as non-linear electrodynamics creating monopoles, quadrupoles, etc. in the metric potentials. We compute the invariants associated with the black holes and show that, when compared to Schwarzschild or Reissner-Nordstr\"om space-times, they have a soft singularity. Also, it is possible to demonstrate that these black holes give rise to three horizons in AdS space-time and two horizons in dS space-time. Finally, thermodynamic quantities can be derived and we show that the solution can be stable or unstable depending on a critical value of the temperature., Comment: 28 pages three figures, will appear in Class.& Quant. Grav

By utilizing the field equations of the modified teleparallel equivalent of general relativity, denoted as $\mathit{f(T)}$, we obtain an exact solution for a static charged black hole in n-dimensions, without imposing any constraints. The black hole possesses two distinctive dimensional constants: $m$ and $v$ with unit {\textit length}. The first constant is associated with the mass, while the second constant represents the electric charge. The existence of this electrical charge causes the black hole to diverge from the expectations of the teleparallel equivalent of general relativity (TEGR). Our analysis demonstrates that $\mathit{f(T)}$ is reliant on the parameter $v$ and transforms into a constant expression when $v$ is assigned a value of zero. A captivating aspect of this particular black hole is its absence of singularities in the quantities formed using torsion and curvature, given that the dimension $n$ falls within the interval of $4 \leq n \leq 6$ as $r$ approaches zero. However, for $n\geq7$, the singularity becomes milder in comparison to the case of TEGR. Furthermore, By utilizing the conserved n-momentum vector, we calculate the energy of this solution and confirm its correspondence with the ADM mass, accurate to the order of $O\Big(\frac{1}{r}\Big)$. Otherwise, we observe higher-order contributions arising from the electric charge terms. Through the application of a coordinate transformation to the black hole, we derive a precise solution describing a stationary rotating black hole. This solution showcases significant readings of the torsion scalar and the analytical function $\mathit{f(T)}$. In order to gain insight into the physics of this black hole, we calculate various physical quantities related to thermodynamics, such as entropy, Hawking temperature, and heat capacity. The analysis reveals that the black hole exhibits thermal stability., Comment: 17 pages and four figures

Many physically inspired general relativity (GR) modifications predict significant deviations in the properties of spacetime surrounding massive neutron stars. Among these modifications is $f(\mathcal{R}, \mathbb{T})$, where $\mathcal{R}$ is the Ricci scalar, $\mathbb{T}$ represents the trace of the energy-momentum tensor, the gravitational theory that is thought to be a neutral extension of GR. Neutron stars with masses above 1.8 $M_\odot$ expressed as radio pulsars are precious tests of fundamental physics in extreme conditions unique in the observable universe and unavailable to terrestrial experiments. We obtained an exact analytical solution for spherically symmetric anisotropic perfect-fluid objects in equilibrium hydrostatic using the frame of the form of $f(\mathcal{R},\mathbb{T})=\mathcal{R}+\beta \mathbb{T}$ where $\beta$ is a dimensional parameter. We show that the dimensional parameter $\beta$ and the compactness, $C=\frac{ 2GM}{Rc^2}$ can be used to express all physical quantities within the star. We fix the dimensional parameter $\beta$ to be at most. (Here ${\mathrm \kappa^2}$ is the coupling constant of Einstein which is figured as $\kappa^2=\frac{8\pi G}{c^4}$, the Newtonian constant of gravitation is denoted as $G$ while $c$ represents the speed of light.) $\beta_1=\frac{\beta}{\kappa^2}= 0.1$ in positive values through the use of observational data from NICER and X-ray Multi-Mirror telescopes on the pulsar PSR J0740+6620, which provide information on its mass and radius., Comment: 22 pages 10 figures

The slow rotation of Kerr-NUT spacetime is explored by taking into account the linear form of rotation and NUT parameters in the dynamical Chern-Simon gravity theory, which can be formulated from a scalar field describing the background. We show that in the absence of the potential scalar field, the metric potential does not respect the effect of the NUT parameter, although the scalar field is affected by the rotation and NUT parameters. Consequently, unlike the gradually spinning black hole solution outlined in \cite{Alexander:2009tp}, the mixed component of the metric potential, encompassing both rotational and NUT parameters, doesn't make a contribution at the primary level of the initial perturbation., Comment: 14 pages

Recently, the mimetic gravitational theory has gained much attention in the frame of cosmology as well as in the domain of astrophysics. In this study, we show that in the frame of mimetic gravitation theory we are not able to derive an isotropic model. As a result, our focus shifts towards combining mimetic gravitational theory with the Lagrangian multiplier. The field equations of a static isotropic gravitational system that controls the geometry and dynamics of star structure are studied in the frame of mimetic theory coupled with a Lagrangian multiplier using a non-linear equation of state. An energy density is assumed from where all the other unknowns are fixed and a new isotropic model is derived. The physical analysis of this model is studied from different viewpoints and consistent results compatible with a realistic isotropic star are investigated analytically and graphically. Ultimately, we demonstrate the stability of the model in question by employing the adiabatic index technique., Comment: 12 pages 6 figures

In the framework of scalar-Einstein-Gauss-Bonnet gravity, we construct the model which realizes the Hayward black hole and discuss the absence of ghosts in this model. Because Hayward black hole has two horizons but no curvature singularity, it may solve the problem of the information loss that might be generated by black holes. The Gauss-Bonnet term appears as a stringy correction, and therefore, our results might indicate that the stringy correction would solve the information loss problem., Comment: 13 pages 2 figures, To appear in Phys. Rev. D

We apply quadratic $f(R)=R+\epsilon R^2$ field equations, where $\epsilon$ has a dimension [L$^2$], to static spherical stellar model. We assume the interior configuration is determined by Krori-Barua ansatz and additionally the fluid is anisotropic. Using the astrophysical measurements of the pulsar PSR J0740+6620 as inferred by NICER and XMM observations, we determine $\epsilon\approx \pm 3$ km$^2$. We show that the model can provide a stable configuration of the pulsar PSR J0740+6620 in both geometrical and physical sectors. We show that the Krori-Barua ansatz within $f(R)$ quadratic gravity provides semi-analytical relations between radial, $p_r$, and tangential, $p_t$, pressures and density $\rho$ which can be expressed as $p_r\approx v_r^2 (\rho-\rho_1)$ and $p_r\approx v_t^2 (\rho-\rho_2)$, where $v_r$ ($v_t$) is the sound speed in radial (tangential) direction, $\rho_1=\rho_s$ (surface density) and $\rho_2$ are completely determined in terms of the model parameters. These relations are in agreement with the best-fit equations of state as obtained in the present study. We further put the upper limit on the compactness, which satisfies the $f(R)$ modified Buchdahl limit. Interestingly, the quadratic $f(R)$ gravity with negative $\epsilon$ naturally restricts the maximum compactness to values lower than Buchdahl limit, unlike the GR or $f(R)$ gravity with positive $\epsilon$ where the compactness can arbitrarily approach the black hole limit $C\to 1$. The model predicts a core density a few times the saturation nuclear density $\rho_{\text{nuc}} = 2.7\times 10^{14}$ g/cm$^3$, and a surface density $\rho_s > \rho_{\text{nuc}}$. We provide the mass-radius diagram corresponding to the obtained boundary density which has been shown to be in agreement with other observations., Comment: 18 pages, 9 figures and one table

Recent findings from the Neutron Star Interior Composition Explorer (NICER) have opened up opportunities to investigate the potential coupling between matter and geometry, along with its resulting physical implications. Millisecond pulsars serve as an ideal subject for conducting such tests and examining these phenomena. We apply the field equations of modified gravity, $f(R, T)=R+\alpha\, T$ to a spherically symmetric spacetime, where $R$ is the Ricci scalar, $\alpha$ is a dimensional parameter, and $T$ is the matter of the geometry. Five unknown functions are present in the output system of differential equations, which consists of three equations. To close the system, we make explicit assumptions about the anisotropy and the radial metric potential, $g_{rr}$. We then solve the output differential equations and derive the explicit forms of the components of the energy-momentum tensor, namely, density, radial, and tangential pressures., Comment: 22 pages, 10 figures, 3 tables

We investigate how to derive an isotropic stellar model in the framework of mimetic gravitational theory. Recently, this theory has gained big interest due to its difference from Einstein's general relativity (GR), especially in the domain non-vacuum solutions. In this regard, we apply the field equation of mimetic gravitational theory to a spherically symmetric ansatz and obtain an over determined system of non-linear differential equations in which differential equations are less than the unknown functions. To overcome the over determined system we suppose a specific form of the temporal component of the metric potential, $g_{tt}$, and assume the vanishing of the anisotropic condition to derive the form of the spatial component of the metric, $g_{rr}$. In this regard, we discuss the possibility to derive a stellar isotropic model that is in agreement with observed pulsars. To examine the stability of the isotropic model we use the Tolman-Oppenheimer-Volkoff equation and the adiabatic index. Furthermore, we assess the model's validity by evaluating its compatibility with a broad range of observed pulsar masses and radii. We demonstrate that the model provides a good fit to these observations., Comment: 13 pages, four figures and two tables

The Chern-Simons (CS) gravity is a modified theory of Einstein's general relativity (GR). The CS theory arises from the low energy limit of string theory which involves anomaly correction to the Einstein-Hilbert action. The CS term is given by the product of the Pontryagin density with a scalar field. In this study, we derive a charged slowly rotating black hole (BH) solution. The main incentives of this BH solution are axisymmetric and stationary and form distortion of the Kerr-Newman BH solution with a dipole scalar field. Additionally, we investigate the asymptotic correction of the metric with the inverse seventh power of the radial distance to the BH solution, This indicates that it will escape any meaningful constraints from weak-field experiments. To find this kind of BHs by observations, we investigate the propagation of the photon near the BH and we show that the difference between the left-rotated polarization and the right-handed one could be observed as stronger than the case of the Kerr-Newman BH. Finally, we derived the stability condition using the geodesic deviations., Comment: 20 pages 3 figures, will appear in Phys. Rev. D

One of the most crucial areas of gravity research, after the direct observation of gravitational waves, is the possible modification of General Relativity at ultraviolet and infrared scales. In particular, the possibility of parity violation should be considered in strong field regime. The Chern-Simons gravity takes into account parity violation in strong gravity regime. For all conformally flat spacetimes and spacetimes with a maximally symmetric two-dimensional subspace, Chern-Simons gravity is identical to General Relativity. Specifically, the Anti-de Sitter (A)dS-Kerr/Kerr black hole is not a solution for Chern-Simons gravity. The slow-rotating BH and the quadratic order in spin solutions are some of the known solutions to quadratic order in spin and they are rotating solutions in the frame of dynamical Chern-Simons gravity. In the present study, for the (A)dS slow-rotating situation (correct to the first order in spin), we derive the linear perturbation equations controlling the metric and the dynamical Chern-Simons field equation corrected to the linear order in spin and to the second order in the Chern-Simons coupling parameter. We show that the black hole of the (A)dS-Kerr solution is stronger (i.e. more compact and energetic) than the Kerr black hole solution and the reason for this feature comes form contributions at Planck scales. Moreover, we calculate the thermodynamical quantities related to this black hole. Finally, we calculate the geodesic equation and derive the effective potential of the black hole., Comment: 15 pages 3 figures, will appear in Phys. Rev D

We show that the spherically symmetric { black hole (BH)} solution of a charged (linear case) field equation of Rastall gravitational theory is not affected by the Rastall parameter and this is consistent with the results presented in the literature. However, when we apply the field equation of Rastall's theory to a special form of nonlinear electrodynamics (NED) source, we derive a novel spherically symmetric BH solution that involves the Rastall parameter. The main source of the appearance of this parameter is the trace part of the NED source, which has a non-vanishing value, unlike the linear charged field equation. We show that the new BH solution is just Anti-de-Sitter Reissner-Nordstr\"om spacetime in which the Rastall parameter is absorbed into the cosmological constant. This solution coincides with Reissner-Nordstr\"om solution in the GR limit, i.e. when Rastall's parameter vanishing. To gain more insight into this BH, we study the stability using the deviation of geodesic equations to derive the stability condition. Moreover, we explain the thermodynamical properties of this BH and show that it is stable, unlike the linear charged case that has a second-order phase transition. Finally, we prove the validity of the first law of thermodynamics., Comment: 12 pages two figures, will appear in Universe Journal

We explore an interior solution of a physically symmetric vierbein with two unknown functions in conformal teleparallel gravity. The field equations can be described in a closed system for a particular form of the metric potentials and an appropriate anisotropic function. As a result, we find a new set of configurations consistent with observed pulsars. In particular, the boundary conditions for the interior spacetime are used for the Schwarzschild spacetime to constrain the conformal field that with a unit value through the surface of a compact object. Furthermore, we apply the present model to the pulsar $4U1608-52$ with approximated radius $R= 9.52 \pm 0.15$ km and mass $M= 1.74 \pm 0.14\, M_{\circledcirc}$. To analyze the stability, we also study the causality conditions and the adiabatic index by assuming the Tolman-Oppenheimer-Volkov equation, adiabatic index and the static state. Moreover, the consistency of the model under consideration with other pulsars is investigated., Comment: 19 pages, 5 figures, will appear in Progress of Theoretical & Experimental Physics

We investigated Rastall gravity, for an anisotropic star with a static spherical symmetry, whereas the matter-geometry coupling as assumed in Rastall Theory (RT) is expected to play a crucial role in differentiating RT from General Relativity (GR). Indeed, all the obtained results confirm that RT is not equivalent to GR, however, it produces the same amount of anisotropy as GR for static spherically symmetric stellar models. We used the observational constraints on the mass and the radius of the pulsar \textit{Her X-1} to determine the model parameters confirming the physical viability of the model. We found that the matter-geometry coupling in RT allows slightly less size than GR for a given mass. We confirmed the model viability via other twenty pulsars' observations. Utilizing the strong energy condition we determined an upper bound on compactness $U_\text{max}\sim 0.603$, in agreement with the Buchdahl limit, whereas Rastall parameter $\epsilon=-0.1$. For a surface density compatible with a neutron core at nuclear saturation density, the mass-radius curve allows masses up to $3.53 M_\odot$. We note that there is no equation of state is assumed, however, the model fits well with a linear behavior. We split the twenty pulsars into four groups according to the boundary densities. Three groups are compatible with neutron cores while one group fits perfectly with higher boundary density $8\times 10^{14}$ g/cm$^3$ which suggests that those pulsars may have quark-gluon cores., Comment: 19 pages, 9 figures

The Chern-Simons amended gravity theory appears as a low-energy effective theory of string theory. The effective theory includes an anomaly-cancelation correction to the Einstein-Hilbert action. The Chern-Simons expression consists of the product $\varphi R \tilde R $ of the Pontryagin density $R \tilde R $ with a scalar field $\varphi$, where the latter is considered as a background field (dynamical construction or non-dynamical construction). Many different solutions to Einstein's general relativity continue to be valid in the amended theories. The Kerr metric is, however, considered an exceptional case that raised a search for rotating black hole solutions. We generalize the solution presented in Phys. Rev. D \textbf{77}, 064007 (2008) by allowing the potential $V$ to have a non-vanishing value and we discuss three different cases of the potential, that is, $V=\mathrm{const.}$, $V\propto \varphi$, and $V\propto \varphi^2$ cases. The present study presents, for the first time, novel solutions prescribing rotating black holes in the frame of the dynamical formulation of the Chern-Simons gravity, where we include a potential and generalize the previously derived solutions. We derive the solutions in the slow-rotation limit, where we write the parameter of the slow-rotation expansion by $\varepsilon$. These solutions are axisymmetric and stationary and they give a distortion of the Kerr solution by a dipole scalar field. Moreover, we investigate that the rectification to the metric behaves in the inverse of the fourth order of radial distance from the center of the black hole when $V\propto \varphi$. This suggests that any meaningful limits from the weak-field experiments could be passed., Comment: 20 pages, 2 figures, will appear in JCAP

Among the modified gravitational theories, the ghost-free Gauss-Bonnet (GFGB) theory of gravity has been considered from the viewpoint of cosmology. The best way to check its applicability could be to elicit observable predicts which give guidelines or limitations on the theory, which could be contrasted with the actual observations. In the present study, we derive consistent field equations for GFGB and by applying the equations to a spherically symmetric space-time, we obtain new spherically symmetric black hole (BH) solutions. We study the physical properties of these BH solutions and show that the obtained space-time possesses multi-horizons and the Gauss-Bonnet invariants in the space-time are not trivial. We also investigate the thermodynamical quantities related to these BH solutions and we show that these quantities are consistent with what is known in the previous works. Finally, we study the geodesic equations of these solutions which give the photon spheres and we find the perihelion shift for weak GFGB. In addition, we calculate the first-order GFGB perturbations in the Schwarzschild solution and new BH solutions and show that we improve and extend existing results in the past literature on the spherically symmetric solutions., Comment: LaTeX 18 pages, 4 figures, to appear in Phys. Rev. D

We extract new classes of anisotropic solutions in the framework of mimetic gravity, by applying the Tolman-Finch-Skea metric and a specific anisotropy not directly depending on it, and by matching smoothly the interior anisotropic solution to the Schwarzschild exterior one. Then, in order to provide a transparent picture we use the data from the 4U 1608-52 pulsar. We study the profile of the energy density, as well as the radial and tangential pressures, and we show that they are all positive and decrease towards the center of the star. Furthermore, we investigate the anisotropy parameter and the anisotropic force, that are both increasing functions of the radius, which implies that the latter is repulsive. Additionally, by examining the radial and tangential equation-of-state parameters, we show that they are monotonically increasing, not corresponding to exotic matter. Concerning the metric potentials we find that they have no singularity, either at the center of the star or at the boundary. Furthermore, we verify that all energy conditions are satisfied, we show that the radial and tangential sound speed squares are positive and sub-luminal, and we find that the surface redshift satisfies the theoretical requirement. Finally, in order to investigate the stability we apply the Tolman-Oppenheimer-Volkoff equation, we perform the adiabatic index analysis, and we examine the static case, showing that in all cases the star is stable., Comment: 20 pages 10 figures, will appear in EPJP

We construct spherically symmetric and static solutions in $F(R)$ gravity coupled with electromagnetic fields. The solutions include new types of black holes with electric and magnetic charges. We show that the higher-derivative terms make the curvature singularity much softer than that in the charged black holes in Einstein's general relativity. We calculate some thermodynamical quantities of the obtained black holes like entropy, Hawking radiation, and quasi-local energy and we confirm that the black hole solutions satisfy the first law of thermodynamics. Finally, we study the stability analysis using the odd-type mode and show that there are stable black hole solutions and the radial speed of the parity-odd mode is unit, that is, the speed of light., Comment: LaTeX 20 pages, 9 figures, to appear in Fortschritte der Physik - Progress of Physics

In this study, we address the issue of a spherically symmetrical interior solution to the quadratic form of $f\mathcal{(T)}=\mathcal{T}+\epsilon \mathcal{T}^2$ gravitational theory using a physical tetrad that provides vanishing components of the off-components of the field equation, in contrast to what exists in the current literature. To be able to formulate the resulting differential equation in a closed form, we employ the Krori-Barua (KB) ansatz. Using the KB spacetime form, we derive the analytic form of the energy-density, radial, and tangential pressures and the anisotropic form. All of these quantities are affected by the dimensional parameter $\epsilon$, which causes them to have a noted difference from those given in the frame of Einstein general relativity. The derived model of this study exhibits a non-trivial form of torsion scalar, and it also contains three constants that we drew from the matching of the boundary condition with a line element that also features a non-trivial form of torsion scalar. Having established the physical conditions that are needed for any real stellar, we check our model and show in detail that it bypasses all of these. Finally, we analyze the model's stability utilizing the Tolman-Oppenheimer-Volkoff equation and adiabatic index and show that our model satisfies these., Comment: 17 Pages, 9 figures, 3 tables, Accepted in NPB. arXiv admin note: text overlap with arXiv:2010.06355

We derive non-flat cosmological models for two cases (i.e., dust and radiation) in the context of M{\o}ller's tetradic theory (MTT) of gravitation using the tetrad that creates the non-flat Friedmann-Robertson-Walker (FRW) metric. These two models are affected by the free dimensional parameter, $\lambda$, that characterized MTT, which approaches zero in the flat case for both models. Using standard definitions of thermodynamics, we calculate the radius horizon, Hawking temperature, and entropy of our non-flat models in the framework of cosmology and show the effect of $\lambda$ on open and closed universes. We then use the first law of thermodynamics to construct non-flat cosmological models via the non-extensive thermodynamic approach. The resulting models are affected by $\lambda$ and the extensive parameter, $\delta$, which quantifies the effect of non-extensive thermodynamics. When we set, $\lambda=0$ and $\delta=1$, we return to Einstein's general relativity models. We study the evolution of our models in the presence of collisionless non-relativistic matter and describe precise forms of the dark energy density and equation-of-state parameter constraining the non-extensive thermodynamic parameter. We show that insertion of the non-extensive thermodynamic parameter affects the non-flat FRW universe in a manner that noticeably differs from that observed under normal thermodynamics. We also show that the deceleration of the open universe behaves as dark energy in a future epoch, i.e., when the redshift approaches -1, i.e., $z\approx$-1., Comment: 18 pages, 10 figures, accepted in PDU

In the frame of Gauss-Bonnet gravity and in the limit of $D\to 4$, based on the fact that spherically symmetric solution derived using any of regularization schemes will be the same form as the original theory \cite{Banerjee:2020yhu,Hennigar:2020lsl,Casalino:2020kbt,Aoki:2020lig}, we derive a new interior spherically symmetric solution assuming specific forms of the metric potentials that have two constants . Using the junction condition we determine these two constants. By using the data of the star EXO $1785-248 $, whose mass is $ { M=1.3\pm0.2 \,{\textrm M}_\odot}$ and radius $ { l=8.849\pm0.4\,{\textrm km}}$, we calculate the numerical values of these constants, in terms of the dimensionful coupling parameter of the Gauss-Bonnet term, and eventually, we get real values for these constants. In this regard, we show that the components of the energy-momentum tensor has a finite value at the center of the star as well as a smaller value to the surface of the star. Moreover, we show that the equations of the state behave in a non-linear way due to the impact of the Gauss-Bonnet term. Using the Tolman-Oppenheimer-Volkoff equation, the adiabatic index, and stability in the static state we show that the model under consideration is always stable. Finally, the solution of this study is matched with observational data of other pulsars showing satisfactory results, Comment: 24 pages, Latex, 5 figures, Accepted in Journal of Symmetry

We show that the mimetic theory with the constraint $g^{\rho \sigma}\partial_\rho\phi \partial_\sigma\phi=1$ cannot realize the black hole geometry with the horizon(s). To overcome such issue, we may change the mimetic constraint a little bit by $\omega(\phi) g^{\rho \sigma}\partial_\rho\phi \partial_\sigma\phi=-1,$ where $\omega(\phi)$ is a function of the scalar field $\phi$. As an example, we consider $(2+1)$-dimensional mimetic gravity with the mimetic potential and construct black hole (BH) solutions by using this modified constraint. We study three different classes: In the first class, we assume the Lagrange multiplier and mimetic potential are vanishing and obtain a BH solution that fully matches the BH of GR despite the non-triviality of the mimetic field which ensures the study presented in {\it JCAP 01 (2019) 058}. In the second class, we obtain a BH having constant mimetic potential and a non-trivial form of the Lagrange multiplier. In the third class, we obtain a new BH solution with non-vanishing values of the mimetic field, the Lagrange multiplier, and the mimetic potential. In any case, the solutions correspond to the space-time with only one horizon but we show that the formalism for the constraint works., Comment: 10 pages Accepted in PLB

Recently, it has been supposed that the Einstein-Gauss- Bonnet theory coupled with scalar field (EGBS) maybe appropriately admit physically viable models of celestial phenomena such that the scalar field effect is active in standard four dimensions. We consider the spherically symmetric and static configuration of the compact star and explain the consequences of the EGBS theory in the frame of stellar modeling. In our formulation, for any given static profile of the energy density $\rho$ with the spherical symmetry and the arbitrary equation of state (EoS) of matter, we can construct the model which reproduces the profile. Because the profile of the energy density determines the mass $M$ and the radius $R_s$ of the compact star, an arbitrary relation between the mass $M$ and the radius $R_s$ of the compact star can be realized by adjusting the potential and the coefficient function of the Gauss-Bonnet term in the action of EGBS theory. This could be regarded as a degeneracy between the EoS and the functions characterizing the model, which tells that only the mass-radius relation is insufficient to constrain the model. For example, we investigate a novel class of analytic spherically symmetric interior solutions by the polytropic EoS. We discuss our model in detail and show that it is in agreement with the necessary physical conditions required for any realistic compact star approving that EGBS theory is consistent with observations., Comment: LaTeX 17 pages, version to appear in EPJC

We investigate the stability of motion and the thermodynamics in the case of spherically symmetric solutions in $f(T)$ gravity using the perturbative approach. We consider small deviations from general relativity and we extract charged black hole solutions for two charge profiles, namely with or without a perturbative correction in the charge distribution. We examine their asymptotic behavior, we extract various torsional and curvature invariants, and we calculate the energy and the mass of the solutions. Furthermore, we study the stability of motion around the obtained solutions, by analyzing the geodesic deviation, and we extract the unstable regimes in the parameter space. We calculate the inner (Cauchy) and outer (event) horizons, showing that for larger deviations from general relativity or larger charges, the horizon disappears and the central singularity becomes a naked one. Additionally, we perform a detailed thermodynamic analysis examining the temperature, entropy, heat capacity and Gibb's free energy. Concerning the heat capacity we find that for larger deviations from general relativity it is always positive, and this shows that $f(T)$ modifications improve the thermodynamic stability, which is not the case in other classes of modified gravity., Comment: 16 pages, 8 figures, version published in JCAP

In this paper, we employ the {\bf mimetic-like} field equations coupled with the Lagrange multiplier and %mimetic {\bf potential} to derive non-trivial spherically symmetric black hole (BH) solutions. We divided this study into three cases: The first one in which we take the Lagrange multiplier and %mimetic {\bf the potential} to have vanishing value and derive a BH solution that completely coincides with the BH of the Einstein general relativity despite the non-vanishing value of the {\bf mimetic-like scalar field}. The first case is completely consistent with the previous studies in the literature that mimetic theory coincides with GR \cite{Nashed:2018qag}. In the second case, we derive a solution with a constant value of the {\bf potential} and a dynamical value of the Lagrange multiplier. This solution has no horizon and therefore the obtained spacetime does not correspond to the BH. In this solution, there appears the region of the Euclidian signature where the signature of the diagonal components of the metric is $(+,+,+,+)$ or the region with two times where the signature is $(+,+,-,-)$. Finally, we derive a BH solution with non-vanishing values of the Lagrange multiplier, {\bf potential}, and {\bf mimetic-like scalar field}. This BH shows a soft singularity compared with the Einstein BH solution. The relevant physics of the third case is discussed by showing their behavior of the metric potential at infinity, calculating their energy conditions, and study their thermodynamical quantities. We give a brief discussion on how our third case can generate a BH with three horizons as in the de Sitter-Reissner-Nordstr\"om black hole spacetime, where the largest horizon is the cosmological one and two correspond to the outer and inner horizons of the BH. Even in the third case, there appears the region of the Euclidian signature or the region with two times., Comment: 14 pages, 12 figures. arXiv admin note: text overlap with arXiv:2107.13550

We construct two new classes of analytical solutions in three-dimensional spacetime and in the framework of $f(R)$ gravity. The first class represents a non-rotating black hole (BH) while the second class corresponds to a rotating BH solution. The Ricci scalar of these BH solutions have non-trivial values and are described by the gravitational mass $M$, two angular momentums $J$ and $J_1$, and an effective cosmological constant $\Lambda_{eff}$. Moreover, these solutions do not restore the $3$-dimensional Ba\~{n}ados-Teitelboim-Zanelli (BTZ) solutions of general relativity (GR) which implies the novelty of the obtained BHs in $f(R)$ gravity. Depending on the range of the parameters, these solutions admit rotating/non-rotating asymptotically AdS/dS BH interpretation in spite that the field equation of $f(R)$ has no cosmological constant. Interestingly enough, we observe that in contrast to BTZ solution which has only causal singularity and scalar invariants are constant everywhere, the scalar invariants of these solutions indicate strong singularity for the spacetime. Furthermore, we construct the forms of the $f(R)$ function showing that they behave as polynomial functions. Finally, we show that the obtained solutions are stable from the viewpoint that heat capacity has a positive value, and also from the condition of Ostrogradski which state that the second derivative of $f(R)$ should have a positive value., Comment: 20 pages Latex

In this paper, we consider the mimetic gravitational theory to derive a novel category of anisotropic star models. To end and to put the resulting differential equations into a closed system, the form of the metric potential $g_{rr}$ as used by Tolman (Tolman 1939) is assumed as well as a linear form of the equation-of-state. The resulting energy-momentum components, energy-density, and radial and tangential pressures contain five constants; three of these are determined through the junction condition, matching the interior with the exterior Schwarzschild solution the fourth is constrained by the vanishing of the radial pressure on the boundary and the fifth is constrained by a real compact star. The physical acceptability of our model is tested using the data of the pulsar 4U 1820-30. The stability of this model is evaluated using the Tolman-Oppenheimer-Volkoff equation and the adiabatic index and it is shown to be stable. Finally, our model is challenged with other compact stars demonstrating that it is consistent with those stars., Comment: 18 pages, 7 figures 2 tables

We construct several new classes of black hole (BH) solutions in the context of the mimetic Euler-Heisenberg theory. We separately derive three differently charged BH solutions and their relevant mimetic forms. We show that the asymptotic form of all BH solutions behaves like a flat spacetime. These BHs, either with/without cosmological constant, have the non constant Ricci scalar, due to the contribution of the Euler-Heisenberg parameter, which means that they are not solution to standard or mimetic $f(R)$ gravitational theory without the Euler-Heisenberg non-linear electrodynamics and at the same time they are not equivalent to the solutions of the Einstein gravity with a massless scalar field. Moreover, we display that the effect of the Euler-Heisenberg theory makes the singularity of BH solutions stronger compared with that of BH solutions in general relativity. Furthermore, we show that the null and strong energy conditions of those BH solutions are violated, which is a general trend of mimetic gravitational theory. The thermodynamics of the BH solutions are satisfactory although there appears a negative Hawking temperature under some conditions. Additionally, these BHs obey the first law of thermodynamics. We also study the stability, using the geodesic deviation, and derive the stability condition analytically and graphically. Finally, for the first time and under some conditions, we derived multi-horizon BH solutions in the context of the mimetic Euler-Heisenberg theory and study their related physics., Comment: 19 pages, 9 figures, accepted for publication in Phys. Rev. D

We investigate the solutions of black holes in $f(T)$ gravity with nonlinear power-law Maxwell field, where $T$ is the torsion scalar in teleparalelism. In particular, we introduce the Langranian with diverse dimensions in which the quadratic polynomial form of $f(T)$ couples with the nonlinear power-law Maxwell field. We explore the leverage of the nonlinear electrodynamics on the space-time behavior. It is found that these new black hole solutions tend towards those in general relativity without any limit. Furthermore, it is demonstrated that the singularity of the curvature invariant and the torsion scalar is softer than the quadratic form of the charged field equations in $f(T)$ gravity and much milder than that in the classical general relativity because of the nonlinearity of the Maxwell field. In addition, from the analyses of physical and thermodynamic quantities of the mass, charge and the Hawking temperature of black holes, it is shown that the power-law parameter affects the asymptotic behavior of the radial coordinate of the charged terms, and that a higher-order nonlinear power-law Maxwell field imparts the black holes with the local stability., Comment: 17 pages, 6 figures, Accepted for publication in Physics of the Dark Universe

In this paper, we shall consider spherically symmetric spacetime solutions describing the interior of stellar compact objects, in the context of higher-order curvature theory of the f(R) type. We shall derive the non--vacuum field equations of the higher-order curvature theory, without assuming any specific form of the $\mathrm{f(R)}$ theory, specifying the analysis for a spherically symmetric spacetime with two unknown functions. We obtain a system of highly non-linear differential equations, which consists of four differential equations with six unknown functions. To solve such a system, we assume a specific form of metric potentials, using the Krori-Barua ansatz. We successfully solve the system of differential equations, and we derive all the components of the energy-momentum tensor. Moreover, we derive the non-trivial general form of $\mathrm{f(R)}$ that may generate such solutions and calculate the dynamic Ricci scalar of the anisotropic star. Accordingly, we calculate the asymptotic form of the function $\mathrm{f(R)}$, which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in \cite{Nashed:2019tuk}, with the latter also resulting in a non-trivial form of the Ricci scalar. Notably but rather expected, the exterior solution differs from the Schwarzschild one in the context of general relativity. The matching procedure will eventually relate two constants with the mass and radius of the compact stellar object. We list the necessary conditions that any compact anisotropic star must satisfy and explain in detail that our model bypasses all of these conditions for a special compact star $\textit {Her X--1 }$, which has an estimated mass and radius \textit {(mass = 0.85 $\pm 0.15M_{\circledcirc}$\,\, and\, \,radius $= 8.1 \pm 0.41$km)}., Comment: 16 pages, 12 figures, 3 tables

We derive a new interior solution for stellar compact objects in $f\mathcal{(R)}$ gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the metric and the first derivative of $f\mathcal{(R)}$. After, the time component of the metric potential and the form of $f(\mathcal R)$ function are derived. From these results, it is possible to obtain the radial and tangential components of pressure and the density. The resulting interior solution represents a physically motivated anisotropic neutron star model. It is possible to match it with a boundary exterior solution. From this matching, the components of metric potentials can be rewritten in terms of a compactness parameter $C$ which has to be $C=2GM/Rc^2 <<0.5$ for physical consistency. Other physical conditions for real stellar objects are taken into account according to the solution. We show that the model accurately bypasses conditions like the finiteness of radial and tangential pressures, and energy density at the center of the star, the positivity of these components through the stellar structure, and the negativity of the gradients. These conditions are satisfied if the energy-conditions hold. Moreover, we study the stability of the model by showing that Tolman-Oppenheimer-Volkoff equation is at hydrostatic equilibrium. The solution is matched with observational data of millisecond pulsars with a withe dwarf companion and pulsars presenting thermonuclear bursts., Comment: 22 pages, 9 figures

In \cite{Bahamonde:2019zea}, a spherically symmetric black hole (BH) was derived from the quadratic form of $f(T)$. Here we derive the associated energy, invariants of curvature, and torsion of this BH and demonstrate that the higher-order contribution of torsion renders the singularity weaker compared with the Schwarzschild BH of general relativity (GR). Moreover, we calculate the thermodynamic quantities and reveal the effect of the higher--order contribution on these quantities. Therefore, we derive a new spherically symmetric BH from the cubic form of $f(T)=T+\epsilon\Big[\frac{1}{2}\alpha T^2+\frac{1}{3}\beta T^3\Big]$, where $\epsilon<<1$, $\alpha$, and $\beta$ are constants. The new BH is characterized by the two constants $\alpha$ and $\beta$ in addition to $\epsilon$. At $\epsilon=0$ we return to GR. We study the physics of these new BH solutions via the same procedure that was applied for the quadratic BH. Moreover, we demonstrate that the contribution of the higher-order torsion, $\frac{1}{2}\alpha T^2+\frac{1}{3}\beta T^3$, may afford an interesting physics., Comment: 18 pages, 6 figures, 1 table

With the successes of $f(R)$ theory as a neutral modification of Einstein's general relativity (GR), we continue our study in this field and attempt to find general %natural { neutral} and charged black hole (BH) solutions. In the previous papers \cite{Nashed:2020mnp,Nashed:2020tbp}, we applied the field equation of the $f(R)$ gravity to a spherically symmetric space-time $ds^2=-U(r)dt^2+\frac{dr^2}{V(r)}+r^2 \left( d\theta^2+\sin^2\theta d\phi^2 \right)$ with unequal metric potentials $U(r)$ and $V(r)$ and with/without electric charge. {Then we have obtained equations which include all the possible static solutions with spherical symmetry.} To ensure the closed form of system of the resulting differential equations in order to obtain specific solutions, we assumed the derivative of the $f(R)$ with respect to the scalar curvature $R$ to have a form %$F_1(r)=\frac{df(R(r))}{dR(r)} \propto %{\color{red} 1 +} %\frac{c}{r^n}$ but in case $n>2$, the resulting black hole solutions with/without charge do not %generate asymptotically GR BH solutions in the limit $c\rightarrow 0$ which means that the only case that can generate GR BHs is $n=2$. %In this paper, we assume another form, i.e., $F_1(r) {=\frac{df(R(r))}{dR(r)} } = 1-\frac{F_0-\left(n-3\right)}{r^n}$ with a constant $F_0$ and show that we can generate asymptotically GR BH solutions for $n>2$ but we show that the $n=2$ case is not allowed. This form of $F_1(r)$ could be the most acceptable physical form that we can generate from it physical metric potentials that can have a well-known asymptotic form and we obtain the metric of the Einstein general relativity in the limit of $F_0\to n-3$. We show that the form of the electric charge depends on $n$ and that $n\neq 2$.}, Comment: LaTeX 18 pages, 16 figures, several revisions

It is known that general relativity (GR) theory is not consistent with the latest observations. The modified gravity of GR known as $\mathrm{f(R)}$ where $\mathrm{R}$ is the Ricci scalar, is considered to be a good candidate for dealing with the anomalies present in classical GR. In this context, we study static rotating uncharged anti-de Sitter and de Sitter (AdS and dS) black holes (BHs) using $\mathrm{f(R)}$ theory without assuming any constraints on the Ricci scalar or on $\mathrm{f(R)}$. We derive BH solutions depend on the convolution function and deviate from the AdS/dS Schwarzschild BH solution of GR. Although the field equations have no dependence on the cosmological constant, the BHs are characterized by an effective cosmological constant that depends on the convolution function. The asymptotic form of this BH solution depends on the gravitational mass of the system and on extra terms that lead to BHs being different from GR BHs but to correspond to GR BHs under certain conditions. We also investigate how these extra terms are responsible for making the singularities of the invariants milder than those of the GR BHs. We study some physical properties of the BHs from the point of view of thermodynamics and show that there is an outer event horizon in addition to the inner Cauchy horizons. Among other things, we show that our BH solutions satisfy the first law of thermodynamics. To check the stability of these BHs we use the geodesic deviations and derive the stability conditions. Finally, using the odd-type mode it is shown that all the derived BHs are stable and have a radial speed equal to one., Comment: 13 pages, 8 figures. arXiv admin note: text overlap with arXiv:2012.05711

We show, in detail, that the only non-trivial black hole (BH) solutions for a neutral as well as a charged spherically symmetric space-times, using the class ${\textit F(R)}={\textit R}\pm{\textit F_1 (R)} $, must-have metric potentials in the form $h(r)=\frac{1}{2}-\frac{2M}{r}$ and $h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}$. These BHs have a non-trivial form of Ricci scalar, i.e., $R=\frac{1}{r^2}$ and the form of ${\textit F_1 (R)}=\mp\frac{\sqrt{\textit R}} {3M} $. We repeat the same procedure for (Anti-)de Sitter, (A)dS, space-time and got the metric potentials of neutral as well as charged in the form $h(r)=\frac{1}{2}-\frac{2M}{r}-\frac{2\Lambda r^2} {3} $ and $h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}-\frac{2\Lambda r^2} {3} $, respectively. The Ricci scalar of the (A)dS space-times has the form ${\textit R}=\frac{1+8r^2\Lambda}{r^2}$ and the form of ${\textit F_1(R)}=\mp\frac{\textit 2\sqrt{R-8\Lambda}}{3M}$. We calculate the thermodynamical quantities, Hawking temperature, entropy, quasi-local energy, and Gibbs-free energy for all the derived BHs, that behaves asymptotically as flat and (A)dS, and show that they give acceptable physical thermodynamical quantities consistent with the literature. Finally, we prove the validity of the first law of thermodynamics for those BHs., Comment: 12 pages, 16 figures

Recent observation shows that general relativity (GR) is not valid in the strong regime. $\mathit{f(R)}$ gravity where $\mathit{R}$ is the Ricci scalar, is regarded to be one of good candidates able to cure the anomalies appeared in the conventional general relativity. In this realm, we apply the equation of motions of $\mathit{f(R)}$ gravity to a spherically symmetric spacetime with two unknown functions and derive original black hole (BH) solutions without any constrains on the Ricci scalar as well as on the form of $\mathit{f(R)}$ gravity. Those solutions depend on a convolution function and are deviating from the Schwarzschild solution of the Einstein GR. These solutions are characterized by the gravitational mass of the system and the convolution function that in the asymptotic form gives extra terms that are responsible to make such BHs different from GR. Also, we show that these extra terms make the singularities of the invariants much weaker than those of the GR BH. We analyze such BHs using the trend of thermodynamics and show their consistency with the well known quantities in thermodynamics like the Hawking radiation, entropy and quasi-local energy. We also show that our BH solutions satisfy the first law of thermodynamics. Moreover, we study the stability analysis using the odd-type mode and shows that all the derived BHs are stable and have radial speed equal to one. Finally, using the geodesic deviations we derive the stability conditions of these BHs., Comment: 21 pages, 21 figures, will appear in Phys. Rev. D. arXiv admin note: text overlap with arXiv:2010.04701