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In this paper, we explore analytic solutions of self-gravitating celestial objects known as gravastars in energy–momentum squared gravity. A gravastar is referred as an alternative model to a black hole which is exhibited by three different regions, i.e., the intermediate shell, interior, and exterior regions. We examine these regions for a particular model of this gravity with conformal motion. The field equations are developed with perfect fluid for a spherically symmetric spacetime. The mathematical formulation for these domains is expressed by using a barotropic equation of state. We use Israel matching conditions for the smooth joining of outer and inner spacetimes. We analyze various physical features of gravastars along with the thickness of the shell, i.e., equation of state parameter, proper length, entropy and energy. These characteristics represent physically consistent non-singular solutions.

This paper explains why spacetime singularities do not constitute a breakdown of physical laws, and points out that the difference between the metrics at singularities and those outside of singularities is factual, rather than nomological.

The main aim of our study is to explore some relativistic configurations of compact object solution in the background of f R gravity, by adopting the Krori-Barua spacetime. In this regard, we establish the field equations for spherically symmetric spacetime along with charged anisotropic matter source by assuming the specific form of the metric potentials, i.e., ν r = B r 2 + C and λ r = A r 2 . Further, to calculate the constant values, we consider the Bardeen model as an exterior spacetime at the surface boundary. To ensure the viability of the f R gravity model, the physical characteristics including energy density, pressure components, energy bonds, equilibrium condition, Herrera cracking concept, mass-radius relation, and adiabatic index are analyzed in detail. It is observed that all the outcomes by graphical exploration and tabular figures show that the Bardeen black hole model describes the physically realistic stellar structures.

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 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 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 f (R) , which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in [1], with the latter also resulting to 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 Her X- - 1, which has an estimated mass and radius (mass=0.85±0.15M⊚andradius=8.1±0.41km). Moreover, we study the stability of this model by using the Tolman–Oppenheimer–Volkoff equation and adiabatic index, and we show that the considered model is different and more stable compared to the corresponding models in the context of general relativity., This work was supported by MINECO (Spain), project PID2019-104397GB-I00 and PHAROS COST Action (CA16214) (SDO).

In this paper, we investigate the existence of anisotropic compact stellar structures in the framework of f ( G , T ) gravity. We assume static spherically symmetric spacetime and utilize the embedding class-I approach to evaluate the unknown metric functions corresponding to a particular f ( G , T ) model. We determine the unknown constants by matching the interior and exterior geometries. The viability of the model is checked for different compact stars through energy bounds, compactness, gravitational redshift, Heintzmann condition for adiabatic index and Herrera stability condition but the graphical analysis is given only for SAX J1808.4-3658 compact star candidate. The behavior of physical parameters indicates viable and stable structure of the stellar model.

We study the gravitation effects on a static and spherically symmetric spacetime due to the vacuum expectation value (VEV) of a Kalb-Ramond field. The Kalb-Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb-Ramond (VEV) and the Ricci tensor, we obtain an exact parameter-dependent power-law modified black hole. For a particular choice of the LSB parameter, the Lorentz violation produces a solution similar to the Reissner-Nordstrom, despite the absence of charge. The near-horizon geometry is modified by including a new inner horizon and shifting the Schwarzschild horizon. Asymptotically, the usual Minkowski spacetime with a background tensor field is recovered. The vacuum configurations are studied considering the energy conditions and the Lorentz violating source properties. By means of the mercury perihelion test, an upper bound to the local Lorentz violation (LV) is obtained, and its corresponding effects on the black hole temperature is investigated., 9 pages. Published version

In this paper, we have developed a static charged anisotropic stellar model for a spherically symmetric spacetime geometry. For this, we have considered charged Durgapal V perfect fluid sphere and constructed its anisotropic counterpart by using gravitational decoupling through the minimal geometric deformation (MGD) approach. We have presented physical analysis of the constructed model in details by taking observational data of two different compact stars, namely, SMC X-4 and Vela X-1, into account. All the physical properties such as density, pressure, sound speeds, energy conditions, stability conditions, Tolman–Oppenheimer–Volkoff (TOV) equation, compactness factor, and redshift are found to meet the general criteria required to ensure a well-behaved stellar system.

We study the effect of gravity on neutrino flavor oscillations when each mass eigenstate is described by a wave packet instead of a plane wave. Two different approaches for implementing the wave packet formalism in the study of neutrino flavor oscillations in curved spacetime are examined. We work with a general static and spherically symmetric spacetime before applying our results to a few spacetime metrics of interest. We first focus on general relativity by examining the effect of the exterior and interior Schwarzschild solutions, as well as the de Sitter-Schwarzschild metric, and then we examine selected metrics from modified gravity models., Comment: 31 pages. 1 figure

We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution, a combination of viscous barotropic fluid, null dust and a null string fluid is also found in a spherically symmetric spacetime. This new system of equations comprises the energy conditions that are satisfied by a Type I fluid. The energy conditions for a Type II fluid are also presented, which are reducible to the Type I fluid only for a particular function. This treatment will assist in studying the complexity of composite relativistic fluids in particular self-gravitating systems.

Starting from a regular, static and spherically symmetric spacetime, we present a stellar model formed by two sources of ordinary and quintessence matter both with anisotropic pressures. The ordinary matter, with density [Formula: see text], is formed by a fluid with a state equation type Chaplygin [Formula: see text] for the radial pressure. And the quintessence matter, with density [Formula: see text], has a state equation [Formula: see text] for the radial pressure and [Formula: see text] for the tangential pressure with [Formula: see text]. The model satisfies the required conditions to be physically acceptable and additionally the solution is potentially stable, i.e. [Formula: see text] according to the cracking concept, and it also satisfies the Harrison–Zeldovich–Novikov criteria. We describe in a graphic manner the behavior of the solution for the case in which the mass is [Formula: see text] and radius [Formula: see text][Formula: see text]km which matches the star EXO 1785-248, from where we obtain the maximum density [Formula: see text] for the values of the parameters [Formula: see text], [Formula: see text].

The present work discusses about the existence of compact star model in the context of $f(R,T)$ gravity with $R$ as the Ricci scalar and $T$ as the trace of energy-momentum tensor $T_{\mu \nu}$. The model has been developed by considering the spherically symmetric spacetime consisting of isotropic fluid with $f(R,T)=R+2 \beta T$ with $\beta$ be the coupling parameter. The corresponding field equations are solved by choosing well known Finch-Skea {\em ansatz} [Finch, M.R., Skea, J.E.F.:{\it Class. Quantum Gravity} {\bf 6}, 467 (1989)]. For spacetime continuity we elaborate the boundary conditions by considering the exterior region as Schwarzschild metric. The unknown constants appearing in the solution are evaluated for the compact star PSR~J 1614-2230 for different values of coupling constant. The physical properties of the model, e.g., matter density, pressure, stability etc. have been discussed both analytically and graphically. This analysis showed that the geometry and matter are compatible with each other as well as the model is in stable equilibrium in the context of $f(R,\,T)$ modified gravity., Comment: Accepted in International Journal of Geometric Methods in Modern Physics on 25.05.2021

This paper considers a static, spherically symmetric spacetime in the context of teleparallel equivalent of General Relativity coupled to the matter content from nonlinear electrodynamics (NED) supported by gauge-invariant Lagrangians, seeking the feasibility of achieving nonsingular solutions. In this setup, the well-known NED solutions, i.e., the Bardeen and Hayward black holes (BHs) are first examined. Then, some specific dyonic configurations, involving both radial electric and magnetic fields, in the teleparallel gravity framework are analysed. For the special case of a Born-Infeld NED theory, a generalized dyonic Reissner–Nordstrom (RN) solution is obtained in terms of the radial coordinate which exhibits a singular behavior at the origin. Nonetheless, the appearance of a naked singularity is impossible in the adopted Born-Infeld (BI) spacetime. The location and size of horizons depend on the BI parameter, leading to the concept of a hairy BH. However, at infinity it is not distinguishable from a dyonic RNBH characterized only by global charges such as ADM mass, electric and magnetic charges.

We find a new family of exact solutions to the Einstein system of equations with an anisotropic fluid distribution for a spherically symmetric spacetime containing a conformal Killing vector. Simple analytic expressions describe the matter variables and the metric functions which are regular at the centre and the interior of the body. We demonstrate that the new class of exact solutions is physically reasonable and may be utilized to model a compact object. A detailed graphical analysis of the matter variables shows that the criteria for physical acceptability are satisfied. The energy conditions are satisfied, causality is not violated, and the body is stable in terms of cracking, the Harrison–Zeldovich–Novikov stability criterion, and the adiabatic index inequality. It is, therefore, possible to geometrically describe a compact object with a conformal symmetry for an astrophysical application.

This paper investigates wormhole solutions of spherically symmetric spacetime via Noether symmetry approach in f ( R , T ) gravity. For this purpose, we choose f ( R , T ) models appreciating indirect curvature–matter coupling and examine symmetry generators with associated conserved quantities. We determine possible existence of realistic traversable wormhole solutions for both dust as well as non-dust distributions and also study stable behavior of these solutions. For both models, we use constant as well as variable forms of red-shift function. To analyze physical existence of wormhole solutions, we study the behavior of null/weak energy conditions with respect to ordinary as well as effective energy–momentum tensors. It is concluded that there exist physically viable traversable as well as stable wormhole solutions in most of the cases.

We investigate photon surfaces and their stability in a less symmetric spacetime, a general static warped product with a warping function acting on a Riemannian submanifold of codimension two. We find a one-dimensional pseudopotential that gives photon surfaces as its extrema regardless of the spatial symmetry of the submanifold. The maxima and minima correspond to unstable and stable photon surfaces, respectively. It is analogous to the potential giving null circular orbits in a spherically symmetric spacetime. We also see that photon surfaces indeed exist for the spacetimes which are solutions to the Einstein equation. The parameter values for which the photon surfaces exist are specified. As we show finally, the pseudopotential arises due to the separability of the null geodesic equation, and the separability comes from the existence of a Killing tensor in the spacetime. The result leads to the conclusion that photon surfaces may exist even in a less symmetric spacetime if the spacetime admits a Killing tensor., 21 pages, no figure

In 1981 Wyman classified the solutions of the Einstein--Klein--Gordon equations with static spherically symmetric spacetime metric and vanishing scalar potential. For one of these classes, the scalar field linearly grows with time. We generalize this symmetry noninheriting solution, perturbatively, to a rotating one and extend the static solution exactly to arbitrary spacetime dimensions. Furthermore, we investigate the existence of nonminimally coupled, time-dependent real scalar fields on top of static black holes, and prove a no-hair theorem for stealth scalar fields on the Schwarzschild background., 17 pages, 1 figure; minor corrections, more refs, accepted in CQG

The main motivation of this study was to probe the compact stars solution with the help of Karmarkar condition in the background of f(R) theory of gravity. To do so, we assume a viable and realistic f(R) gravity model in the presence of a charged anisotropic fluid sphere along with static spherically symmetric spacetime. Moreover, we consider a specific model of Adler approach for metric potential $$g_{tt}$$ , which shows a new family of solutions and then by using the Karmarkar condition, we obtain the other component of the metric tensor $$g_{rr}$$ . The key feature of our study is to assume the Bardeen model as an exterior geometry. To ensure the viability of f(R) gravity model, we conduct various physical tests like energy density, pressure components, energy bonds, equilibrium condition, Herrera cracking concept, and mass–radius relation. It is observed that all physical attributes follow the physically accepted fact, which confirm the viability and consistency of our model. Our study also shows that the f(R) theory of gravity seems to be an appropriate theory to describe the existence of embedded class-one solutions of compact stars.

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.

We investigate the deflection angle in a strong deflection limit for a marginally unstable photon sphere in a general asymptotically flat, static and spherically symmetric spacetime under some assumptions to calculate observables. The deflection angle of a light ray reflected by the marginally unstable photon sphere diverges nonlogarithmically while the one reflected by a photon sphere diverges logarithmically. We apply our formula to a Reissner-Nordstrom spacetime and Hayward spacetime., Comment: 10 pages, 5 figures, minor correction, title changed, accepted for publication in Physical Review D

A number of near-extremal conditions are utilized to simplify the equation of motion of the neutral scalar perturbations in generalized spherically symmetric black hole background into a differential equation with the P\"{o}schl-Teller potential. An analytic formula for quasinormal frequencies is obtained. The analytic formula is then used to investigate Strong Cosmic Censorship conjectures~(SCC) of the generalized black hole spacetime for the smooth initial data. The Christodoulou version of the SCC is found to be violated for certain regions of the black hole parameter space including the black holes in General Relativity while the $C^{1}$ version of the SCC is always valid., Comment: 39 pages, 9 figures, to appear in EPJC. arXiv admin note: Sections of this work were previously part of arXiv:1911.11448 which is being split

The canonical formalism of a spherically symmetric spacetime has been decomposition with respect to the radial coordinate r in the context of $$3 + 1$$ split of spacetime. We have set up an effective Lagrangian that plays the role of independent variable couple with metric function. The surface gravity of Schwarzschild–de Sitter black hole has been quantized from the test particle moving around different energy states like Bohr’s atomic model. We have quantized the Hawking temperature and entropy of Schwarzschild–de Sitter black hole from quantization of surface gravity. We also have shown that the change of entropy reduced to zero when the boundary shrinks to very small size.

In this article, we demonstrate the weak gravitational lensing in the context of Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole. To this desire, we derive the deflection angle of light in a plasma medium by BBMB black hole using the Gibbons and Werner method. First, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically symmetric spacetime of BBMB black hole. Moreover, we also analyze the graphical behavior of deflection angle by BBMB black hole in the presence of plasma medium., Comment: 5 pages. Accepted for publication in The European Physical Journal Plus

Evidences have been found that the weak cosmic censorship conjecture could be violated if test particles with charge and angular momentum are injected into a black hole. However, second-order corrections and fine-tunings on the particle's parameters are required in previous studies, indicating that self-force and radiative effects must be taken into account. In this paper, we first consider a magnetically charged particle falling into an extremal Bardeen black hole, which is regular (with no singularity) and has a magnetic monopole at the center. We then investigate a general class of magnetic black holes associated with nonlinear electrodynamics. In all the cases, we show that the test particle with magnetic charge could overcharge the black hole, causing possible violation of the weak cosmic censorship conjecture. We also find that every spherically symmetric spacetime associated with a magnetic field can also be generated by an electric field. Moreover, if a magnetically charged black hole can be overcharged, the same spacetime containing an electrically charged black hole can also be overcharged. Although possible counterexamples to the weak cosmic censorship have been constructed previously in the literature, which always involved higher-order terms in particles' parameters, we find, for the first time, that linear terms are enough to make counterexamples.

The present study is devoted to explore the existence of a new family of compact star solutions by adopting the Karmarkar as well as Pandey&ndash, Sharma condition in the background of f ( R , T ) modified gravitational framework. For this purpose, we consider static spherically symmetric spacetime with anisotropic fluid distribution in absence of electric charge. In respect of Karmarkar condition, we assume a specific model of g r r metric potential representing a new family of solutions which is also compatible with the Pandey&ndash, Sharma condition. This assumed model permits us to calculate the g t t component of metric tensor by making the use of Karmarkar condition. Further, we investigate the interior solutions for V e l a X &minus, 1 model of compact star by utilizing this new family of solutions for different values of parameter &lambda, We have tuned the solution for V e l a X &minus, 1 so that the solutions matches the observed mass and radius. For the same star we have extensively discussed the behavior of the solutions. It is found that these solutions fulfill all the necessary conditions under the observational radii and mass attribute data for small values of parameter &lambda, and hence physically well-behaved and promising. Through graphical analysis, it is observed that our obtained analytical solutions are physically acceptable with a best degree of accuracy for n &isin, [ 1 . 8 , 7 ) &minus, { 2 , 4 , 6 } , where parameter n is involved in the discussed model. It is also noticed the causality condition is violated for all n &ge, 7 and the tangential sound velocity v t is observed as complex valued for all 0 &lt, n &lt, 1 . 8 . Likewise, we explore these properties by considering large parameter &lambda, values. It is seen that the presented model violates all the physical conditions for n &isin, { 2 , 4 , 6 } , while some of these for large values of &lambda, Consequently, it can be concluded that the parameters n and &lambda, have a strong impact on the obtained solutions.

The existence of strange matter in compact stars may pose striking sequels of the various physical phenomena. As an alternative to neutron stars, a new class of compact stars called strange stars should exist if the strange matter hypothesis is true. In the present article, we investigate the possible construction of the strange stars in quark matter phases based on the MIT bag model. We consider scenarios in which strange stars have no crusts. Then we apply two types of equations of state to quantify the mass-radius diagram for static strange star models performing the numerical calculation to the modified Tolman-Oppenheimer-Volkoff (TOV) equations in the context of $4D$ Einstein-Gauss-Bonnet gravity. It is worth noting that the GB term gives rise to a non-trivial contribution to the gravitational dynamics in the limit $D \to 4$. However, the claim that the resulting theory is of pure graviton was cast in doubt by several grounds. Thus, we begin our discussion with showing the regularized $4D$ EGB theory has an equivalent action as the novel $4D$ EGB in a spherically symmetric spacetime. We also study the effects of coupling constant $\alpha$ on the physical properties of the constructed strange stars including the compactness and criterion of adiabatic stability. Finally, we compare our results to those obtained from the standard GR., Comment: v2: 16 pages, major modification, regularized 4DEGB scheme added, version accepted for publication by ApJ

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation., Accepted for publication in Physical Review D (https://journals.aps.org/prd/accepted/22076Q27Da314d28369686b12569e1772f8bcf8da)

Using a novel and self-consistent approach that avoids the scalar-tensor identification in the Einstein frame, we reanalyze the viability of f(R) gravity within the context of solar-system tests. In order to do so, we depart from a simple but fully relativistic system of differential equations that describe a compact object in a static and spherically symmetric spacetime, and then make suitable linearizations that apply to non-relativistic objects such as the Sun. We then show clearly under which conditions the emerging chameleon-like mechanism can lead to a Post-Newtonian Parameter γ compatible with the observational bounds. To illustrate this method, we use several specific f(R) models proposed to explain the current acceleration of the Universe, and we show which of them are able to satisfy those bounds., Facultad de Ciencias Astronómicas y Geofísicas

Using a novel and self-consistent approach that avoids the scalar-tensor identification in the Einstein frame, we reanalyze the viability of $f(R)$ gravity within the context of solar-system tests. In order to do so, we depart from a simple but fully relativistic system of differential equations that describe a compact object in a static and spherically symmetric spacetime, and then we make suitable linearizations that apply to nonrelativistic objects such as the Sun. We then show clearly under which conditions the emerging chameleonlike mechanism can lead to a post-Newtonian parameter $\ensuremath{\gamma}$ compatible with the observational bounds. To illustrate this method, we use several specific $f(R)$ models proposed to explain the current acceleration of the Universe, and we show which of them are able to satisfy those bounds.

Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity $v$ in arbitrary static and spherically symmetric spacetimes and in equatorial plane of arbitrary static and axisymmetric spacetimes. We show that the expansion in the large closest approach $x_0$ limit depends on the asymptotic behavior of the metric functions only, and the generated integrand is always integrable, resulting in a deflection angle in a series form of either $x_0$ or $b$, the impact parameter. Using this method, the deflection angles as series of both $x_0$ and $b$ are found in Schwarzschild, Reissner-Nordstr\"{o}m and Kerr-Newman spacetimes to 17-th, 15-th and 6-th orders respectively, for both lightrays and particles with general velocity. The effects of the impact parameter, velocity and other parameters of the spacatimes are briefly analyzed. Moreover, we show that for spacetimes whose metric functions are only asymptotically known, the deflection angle in the weak field limit can also be calculated. Furthermore, it is shown that the deflection angle in general static and spherically symmetric spacetime and equatorial plane of static and axisymmetric spacetime to the lowest non-trivial order, depends only on the impact parameter, velocity of the particle, and the effective ADM mass of the spacetime but not on other parameters such as charge or angular momentum. These deflection angles are used in an exact gravitational lensing equation and the corresponding apparent angles of the images of the source are also solved perturbatively., Comment: 42 pages, 5 figures; typos and grammar corrected; references added

We study motions of photons in an unmagnetized cold homogeneous plasma medium in the five-dimensional charged static squashed Kaluza-Klein black hole spacetime. In this case, a photon behaves as a massive particle in a four-dimensional spherically symmetric spacetime. We consider the light deflection by the squashed Kaluza-Klein black hole surrounded by the plasma in a weak-field limit. We derive corrections of the deflection angle to general relativity, which are related to the size of the extra dimension, the charge of the black hole and the ratio between the plasma and the photon frequencies., Comment: 18 pages, 4 figures

We investigate the behavior of the Dirac spinor fields in general relativistic high density stellar backgrounds and the possibility of spontaneous spinorization which is analogous to spontaneous scalarization. We consider the model with the modified kinetic term of the Dirac field by the insertion of the fifth gamma matrix ${\hat \gamma}^5$ and the conformal coupling of the Dirac spinor field to the matter sector, which would lead to the tachyonic growth of the Dirac spinor field in the high density compact stellar backgrounds. In order to obtain the static and spherically symmetric solutions, we have to consider the two Dirac fields at the same time. We show that in the constant density stellar backgrounds our model gives rise to the nontrivial solutions of the Dirac spinor fields with any number of nodes, where one mode has one more nodes than the other. We also show that at the leading order all the components of the effective energy-momentum tensor of the Dirac spinor fields, after the summation over the two fields, vanish for any separable time-dependent ansatz of the Dirac spinor fields in any static and spherically symmetric spacetime backgrounds, indicating that spontaneous spinorization takes place as a stealth process in the static and spherically symmetric spacetime with any number of nodes, which would be quenched by nonlinear effects and leave no observable effects., Comment: 14 pages, 2 figures, published version

Lorentz violation is motivated by quantum gravity and it is generically described by nondynamical tensors. In this work a Lorentz violating extension of general relativity is studied where a nondynamical tensor couples to the Weyl tensor. A family of static and spherically symmetric solutions in vacuum is found, confirming that there are consistent solutions with explicit Lorentz violation in dynamical spacetimes. These solutions produce an unconventional dependence of the gravitational redshift, which, in turn, leads to the first bounds on such nondynamical tensor that do not rely on the physics of the early universe. Moreover, the bounds obtained in this work are competitive with respect to limits on similar nondynamical tensors., Comment: 6 double-column pages

Based on the geometry of the codimension-2 surface in a general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one by Claudel, Virbhadra, and Ellis but without reference to any umbilical hypersurface in the spacetime. The new definition effectively rules out the photon surface which has noting to do with gravity. The application of the definition to the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse reduces to a problem of a second order differential equation. We find that the energy balance on the boundary of the dust ball can provide one appropriate boundary condition to this equation. Based on this key investigation, we find an analytic photon surface solution in the Oppenheimer-Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model. Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of gravitational field of the system., revtex, 19 pages, 10 figures; v3, references added, one definition is improved, typos are corrected

The main purpose of this paper is to investigates structure scalars in the context of $f(\mathcal{G}, T)$ gravity, where $\mathcal{G}$ is the Gauss-Bonnet invariant and $T$ is the trace of stress energy tensor. For this aim, we have considered the spherically symmetric spacetime and dissipative anisotropic fluid coupled with radiation and heat ejecting shearing matter distributions. We have found these scalar variables by orthogonally decomposing the Riemann curvature tensor in $f(\mathcal{G}, T)$ gravity. Moreover, the evolution equations of shear and expansion are also developed with the help of these scalar functions. We have also analyzed these scalars by taking constant $\mathcal{G}$ and $T$ for dust cloud. The physical behavior of structure scalars for radiating matter distributions has been examined in the presence of modified gravity. It is shown that the evolutionary stages of relativistic stellar structures can be explored via modified scalar functions., Comment: 21 pages, submitted for publication

It is shown that the redshift between two Cauchy surfaces in a globally hyperbolic spacetime equals the ratio of the associated contact forms on the space of light rays of that spacetime., 9 pages, 1 figure

This paper studies the evolutionary mechanism of the relativistic spherically symmetric spacetime who is coupled with both radiating and non-radiating matter content in f ( R , T ) gravity. This modeled system is assumed to obey the constraint of minimal complexity having areal radius velocity to be proportional to the areal radius, i.e., quasi-homologous condition. The corresponding few exact analytical solutions are examined with some realistic background. Our few models described the emergence of Minowskian cavity around the center of the relativistic spherical structure. We also calculated the structure scalars in modified gravity that are gained by splitting the Riemann tensor orthogonally. The structure scalar Y T F e f f is found to the complexity factor. Various realistic applications of our calculated models in relativistic astrophysics are described. •Evolutionary mechanism of relativistic star will be studied in f ( R , T ) gravity.•It obeys the constraint of minimal complexity with quasi-homologous condition.•Some exact analytical solutions are explored with realistic background.

In this paper, the higher-dimensional collapse of homogeneous isotropic perfect fluid is studied by considering the geometry of five-dimensional spherically symmetric metric. Using equations of state for different fields like dust, radiation and stiff fluid with and without cosmological constant [Formula: see text], the gravitational collapse is studied. The results are compared with the usual four-dimensional study in [A. V. Astashenok, K. Mosani, S. D. Odintsov and G. C. Samanta, Int. J. Geom. Methods Mod. Phys. 16, 1950035 (2019)]. It is found that the collapse rate is faster in five-dimensional spacetime as compared to four-dimensional case supporting the cosmic censorship hypothesis.

We present a class of exact spherically symmetric and non-static solutions of Einstein-Maxwell’s field equations. We have assumed isotropic pressure distribution and have taken ansatz on two of the gravitational potentials. The solutions admit negative pressure. We show that the solutions satisfy physical boundary conditions associated with the Einstein-Maxwell exact solutions. Therefore, these solutions can model physical systems such as moving dark energy stars.

We present an Einstein space axially symmetry spacetime admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time machine spacetime. The spacetime is a four-dimensional generalization of flat Misner space in curved spacetime, free-from curvature divergences and belongs to type N in the Petrov classification. The spacetime admits a non-expanding, non-twisting, and shear-free null geodesic congruence.

A new technique is introduced to study the completeness of inextensible electromagnetic trajectories in an n ( ≥ 2 ) -dimensional stationary spacetime. Sufficient conditions on an electromagnetic field on a stationary spacetime are imposed to ensure that the associated ( n + 1 ) -dimensional Kaluza–Klein bundle spacetime is itself stationary. The problem is then reduced to the geodesic completeness of the corresponding Kaluza–Klein bundle spacetime. Applications are given specially to the case of a standard static spacetime.

It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlev\`{e}--Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlev\`{e}--Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints., Comment: 10 pages; Journal version, minor changes