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This article is devoted to the study of the thermodynamics phase transitions and critical phenomena of an FLRW cosmological model under the so-called Kaniadakis's statistics. The equation of state is derived from the corrected Friedmann field equations and the thermodynamics unified first law. This reveals the existence of non-trivial critical points where a first-order phase transition takes place. The system behaves as an "inverted" van der Waals fluid in this concern. Interestingly, the numerical values of the critical exponents are the same as those of the van der Waals system. Besides, to obtain more insights into the thermodynamics description, the so-called Ruppeiner's geometry is studied through the normalized scalar curvature, disclosing this invariant zone where the system undergoes repulsive/attractive interactions. Near the critical point, this curvature provides again the same critical exponent and universal constant value as for van der Waals fluid., Comment: 11 pages, 4 figures. Accepted version at Physics Letter B

For an FLRW model, thermodynamic phase transitions are investigated in the Einstein-Gauss-Bonnet gravity framework. Using the work density, the equation of state is derived, and the criticality conditions are employed to determine the critical points where possible phase transitions occur. The appearance of phase transitions strongly depends upon the space-time dimension $n$. In this concern, for $n=5$, there is a first-order phase transition, a liquid-gas van der Waals-like phase transition, where the Gibbs free energy presents a swallowtail behavior. On the other hand, for $n=6$, the system does not exhibit a first-order van der Waals-like phase transition. In such a case, the Gibbs free energy presents a cusp with stable and unstable branches. For the present study, the mentioned phenomena are present for an expanding cosmology, where the matter distribution filling the Universe corresponds to a speculative matter distribution with an equation of state parameter greater than one. Interestingly, there are no phase transitions for dimensions higher than $n=6$, nor for expanding or contracting cosmological scenarios. To gain more insights into the system, the micro-structure is analyzed using thermodynamic geometry to quantify the normalized scalar curvature. This invariant shows that a repulsive interaction dominates the phase transition region, while the region where the system has a gas-like behavior attractive interaction prevails. Besides, the critical exponents have been obtained, coinciding their numerical values with the universal ones.

Employing the thermodynamic unified first law through the thermodynamic-gravity conjecture, in this article, we derive for a FLRW universe the Friedmann equations in the framework of Gauss-Bonnet gravity theory. To do this, we project this generalized first law along the Kodama vector field and along the direction of an orthogonal vector to the Kodama vector. The second Friedmann equation is obtained by projecting on the Kodama vector, while the first is obtained by projecting along the flux on the Cauchy hypersurfaces. This result does not assume a priory temperature and an entropy, so the Clausius relation is not used here. Nevertheless, it is used to obtain the corresponding Gauss-Bonnet entropy. In this way, the validity of the generalized second law of thermodynamics is proved for the Gauss-Bonnet gravity theory., Comment: 10 pages, 2 figures

In this article, using gravitational decoupling by means of minimal geometric deformation approach, we obtain a new spherically symmetric and static black hole solution. To progress, we close the system by assuming that the average pressure of the $\theta$-sector is vanishing. Also, we tackle the problem regarding how, for a given minimally deformed black hole solution, one can connect it to a wormhole space-time., Comment: 15 pages, 6 figures, Accepted in European Physical Journal C (in press)

We analyze the dispersion relation for an anisotropic gravity-electromagnetic theory at very high energies. In particular for photons of very high energy. We start by introducing the anisotropic gravity-gauge vector field model. It is invariant under spacelike diffeomorphisms, time parametrization, and U(1) gauge transformations. It includes high-order spacelike derivatives as well as polynomial expressions of the Riemann and field strength tensor fields. It is based on the Ho\v{r}ava-Lifshitz anisotropic proposal. We show its consistency, and the stability of the Minkowski ground state. Finally, we determine the exact zone at which the physical degrees of freedom, i.e. the transverse-traceless tensorial degrees of freedom and the transverse vectorial degrees of freedom propagate according to a linear wave equation. This is so, in spite of the fact that there exists in the zone a non-trivial Newtonian background of the same order. The wave equation contains spatial derivatives up to the sixth order, in the lowest order it exactly matches the relativistic wave equation. We then analyze the dispersion relation at very high energies in the context of recent experimental data. The qualitative predictions of the proposed model, concerning the propagation of highly energetic photons, are different from the ones obtained from the modified dispersion relation of the LIV models., Comment: 9 pages, 3 figures

In this article, new wormhole solutions in the framework of General Relativity are presented. Taking advantage of gravitational decoupling by means of minimal geometric deformation approach and, the so-called noncommutative geometry Gaussian and Lorentzian density profiles, the seminal Morris-Thorne space-time is minimally deformed providing new asymptotically wormhole solutions. Constraining the signature of some parameters, the dimensionless constant $\alpha$ is bounded using the flare-out and energy conditions. In both cases, this results in an energy-momentum tensor that violates energy conditions, thus the space-time is threading by exotic matter. However, it is possible to obtain a positive defined density at the wormhole throat and its neighborhood. To further support the study a thoroughly graphical analysis has been performed., Comment: 20 pages, 6 figures. Accepted Version Fortschritte der physik

This work is devoted to provide a way of representing $4D$ spherically symmetric and static compact stellar configurations into a $5D$ space time, using the black string framework. We write the four and five dimensional line elements and the four and five dimensional energy momentum tensor such that the four and five dimensional quantities are related by a function $A(z)$, where $z$ represents to the extra dimension. Remarkably, one consequence of our chosen form for the line element, for the energy momentum tensor and for $A(z)$, is the fact that the $5D$ equations are reduced to the usual form of the four dimensional equations of motion. Also, the five dimensional conservation equation adopts the form of the four dimensional conservation equation. It is worth mentioning that, although our methodology is simple, this form of reduction could serve to represent other types of four dimensional objects into an extra dimension in future works. Furthermore, under our assumptions the sign of the pressure along the extra dimension is given by the trace of the four dimensional energy momentum tensor. Furthermore, our simple election for the function $A(z)$ modifies some features of the induced 4--dimensional compact stellar configuration, such as the mass--radius relation, the momentum of inertia, the central values of the thermodynamic variables, to name a few. Besides, the topology of this model is ${S}^{2}\times {S}^{1}$ and not the ${S}^{3}$ topology of the 5--dimensional structures.

In this paper, we have studied the bouncing behavior of the cosmological models formulated at the background of the Hubble function in the F(R, G) theory of gravity, where R and G denote the Ricci scalar and Gauss-Bonnet invariant. The actions of bouncing cosmology are studied under consideration of different viable models and can resolve the difficulty of singularity in standard Big-Bang cosmology. Both models show bouncing behavior and satisfy the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late evolution time. Phantom at the bounce epoch is analogous to a quintessence behavior. Finally, we formulate the perturbed evolution equations and investigate the stability of two bouncing solutions., Comment: 14 pages, 10 figures

We investigate the possibility of future singularity due to the accelerating expansion of the Universe. It has been found that the gravitational theory comprises Ricci scalar $R$ and Gauss-Bonnet invariant $\mathcal{G}$, known as $F(R,\mathcal{G})$ gravity, which can be viewed in the quadratic form. Three models are presented using Hubble parameters to represent a finite and infinite future. The parameters of the models are analyzed on the basis of their physical and geometrical properties. This study also explores the properties of the modified gravitational theory, and neither the future singularity nor the little or pseudo rip is posed as threats to the fate of the Universe. We present scalar perturbation approaches to perturbed evolution equations and demonstrate their stability., Comment: 14 pages, 12 figures

We consider the anisotropic gravity-gauge vector coupling in the non-projectable Ho\v{r}ava-Lifshitz theory at the kinetic conformal point, in the low energy regime. We show that the canonical formulation of the theory, evaluated at its constraints, reduces to a canonical formulation solely in terms of the physical degrees of freedom. The corresponding reduced Hamilton defines the ADM energy of the system. We obtain its explicit expression and discuss its relation to the ADM energy of the Einstein-Maxwell theory. We then show that there exists, in this theory, a well--defined wave zone. In it, the physical degrees of freedom {\i}.e., the transverse--traceless tensorial modes associated to the gravitational sector and the transverse vectorial modes associated to the gauge vector interaction satisfy independent linear wave equations, without any coupling between them. The Newtonian part of the anisotropic theory, very relevant near the sources, does not affect the free propagation of the physical degrees of freedom in the wave zone. It turns out that both excitations, the gravitational and the vectorial one, propagate with the same speed $\sqrt{\beta}$, where $\beta$ is the coupling parameter of the scalar curvature of the three dimensional leaves of the foliation defining the Ho\v{r}ava--Lifshitz geometry., Comment: 14 pages

This work is devoted to the study of analytic wormhole solutions within the framework of $f(R)$ gravity theory. To check the possibility of having wormhole structures satisfying energy conditions, by means of the class I approach the pair $\{\Phi(r), b(r)\}$ describing the wormhole geometry has been obtained. Then, in conjunction with a remarkably $f(R)$ gravity model, the satisfaction of the null and weak energy conditions at the wormhole throat and its neighborhood is investigated. To do so, some constant parameters have been bounded restricting the space parameter. In this concern, the $f(R)$ gravity model and its derivatives are playing a major role, specially in considering the violation of the non--existence theorem. Furthermore, the shape function should be bounded from above by the Gronwall--Bellman shape function, where the red--shift function plays a relevant role. By analyzing the main properties at the spatial stations and tidal accelerations at the wormhole throat, possibilities and conditions for human travel are explored., Comment: 20 pages, 21 figures

In this paper, we have presented a bouncing cosmological model of the Universe in an extended theory of gravity. The dynamical behaviour of the model obtained from the flat FLRW space-time along with the violation of null energy condition have been shown. The geometrical parameters show singularity behaviour at the bouncing epoch. The parameters involved in the scale factor play a major role in the bouncing behaviour. In addition, the coupling parameter that resulted in the minimal matter-geometry coupling in the extended gravity has significant role to avoid the singularity of equation of state parameter at the bouncing epoch. Using a linear homogeneous perturbation calculation, we show the stability of the model., Comment: 13 pages, 18 figures, Accepted version, Fortschritte der Physik

A spherically symmetric solution of the field equations of the Ho\v{r}ava--Lifshitz gravity--gauge vector interaction theory is obtained and analyzed. It describes a charged throat. The solution exists provided a restriction on the relation between the mass and charge is satisfied. The restriction reduces to the Reissner--Nordstr\"{o}m one in the limit in which the coupling constants tend to the relativistic values of General Relativity. We introduce the correct charts to describe the solution across the entire manifold, including the throat connecting an asymptotic Minkowski space--time with a singular 3+1 dimensional manifold. The solution external to the throat on the asymptotically flat side tends to the Reissner--Nordstr\"{o}m space--time at the limit when the coupling parameter, associated with the term in the low energy Hamiltonian that manifestly breaks the relativistic symmetry, tends to zero. Also, when the electric charge is taken to be zero the solution becomes the spherically symmetric and static solution of the Ho\v{r}ava--Lifshitz gravity.

An anisotropic model describing gravity--vector gauge coupling at all energy scales is presented. The starting point is the 4+1 dimensional non--projectable Ho\v{r}ava--Lifshitz gravity theory subject to a geometrical restriction. Renormalizability arguments require all possible interactions in the potential up to terms with $z=4$ spatial derivatives on the geometrical tensor fields: the Riemann and Weyl tensors. The latter being necessary on a 4+1 dimensional formulation. The dimensional reduction to 3+1 dimensions give rise to a model invariant under {foliation--preserving diffeomorphisms} (FDiff) and $U(1)$ symmetry groups. The reduced theory on the {kinetic conformal} (KC) point ($\lambda =1/3$), propagates the same spectrum of the Einstein--Maxwell theory. Moreover, at low energies, on the IR point $\alpha=0$, $\beta=1$, its field equations are exactly the Einstein--Maxwell ones in a particular gauge condition. The Minkowski ground state is stable provided several restrictions on the coupling parameters are satisfied, they are explicitly obtained. The quantum propagators of the physical degrees of freedom are obtained and after an analysis of the first and second class constraints the renormalizability by power counting is proved, provided that the aforementioned restrictions on the coupling parameters are satisfied.

This research develops a well-established analytical solution of the Einstein-Maxwell field equations. We analyze the behavior of a spherically symmetric and static interior driven by a charged anisotropic matter distribution. The class I methodology is used to close the system of equations and a suitable relation between the anisotropy factor and the electric field is imposed. The inner geometry of this toy model is described using an ansatz for the radial metric potential corresponding to the well-known isotropic Buchdahl space-time. The main properties are explored in order to determine if the obtained model is appropriate to represent a real compact body such as neutron or quark star. {We have fixed the mass and radii using the data of the compact objects} SMC X-1 and LMC X-4. It was found that the electric field and electric charge have magnitudes of the order of $\sim 10^{21}\ [V/cm]$ and $\sim 10^{20}\ [C]$, respectively. The magnitude of the electric field and electric charge depends on the dimensionless parameter $\chi$. To observe these effects on the total mass, mass-radius ratio and surface gravitational red-shift, we computed numerical data for different values of $\chi$.

We provide a new regular black hole solution in $(2+1)$ dimensions with presence of matter fields in the energy momentum tensor, having its core a flat or (A)dS structure. Since the first law of thermodynamics for regular black holes is modified by the presence of the matter fields, we provide a new version of the first law, where a local definition of the variation of energy is defined, and, where the entropy and temperature are consistent with the previously known in literature. It is shown that the signs of the variations of the local definition of energy and of the total energy coincide. Furthermore, at infinite, the usual first law $dM=TdS$ is recovered. It is showed that the formalism used is effective to compute the total energy of regular black holes in $(2+1)$ with presence of matter in the energy momentum tensor. This latter suggests the potential applicability of this formalism to calculate the mass of other models of regular black holes in $d \ge 4$ dimensions., Comment: accepted for publication in EPL

The present article is devoted to the study of local anisotropies effects on the Durgapal's fourth model in the context of gravitational decoupling via the Minimal Geometric Deformation approach. To do it, the most general equation of state relating the components of the $\theta$--sector is imposed to obtain the decoupler function $f(r)$. In addition, certain properties of the obtained solution are investigated, such as the behavior of the salient material content threading the stellar interior, causality and energy conditions, hydrostatic balance through modified Tolman--Oppenheimer--Volkoff conservation equation and stability mechanism against local anisotropies by means of adiabatic index, sound velocity of the pressure waves, convection factor and Harrison--Zeldovich--Novikov procedure, in order to check if the model is physically admissible or not. Regarding the stability analysis, it is found that the model presents unstable regions when the sound speed of the pressure waves and convection factor are used in distinction with what happens in the adiabatic index and Harrison--Zeldovich--Novikov case. To produce a more realistic picture the numerical data for some known compact objects was placed and different values of the parameter $\alpha$ were considered to compare with the GR case \i.e, $\alpha=0$., Comment: To be published in Chinese Physics C

In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential $e^{2\lambda(r)}$ and an equation of state. Specifically, the so-called modified generalized Chaplygin equation of state with $\omega=1$ and depending on two parameters, namely, $A$ and $B$. These ingredients close the problem, at least mathematically. However, to check the feasibility of the model, a complete physical analysis has been performed. Thus, we analyze the obtained geometry and the main physical observables, such as the density $\rho$, the radial $p_{r}$, and tangential $p_{t}$ pressures as well as the anisotropy factor $\Delta$. Besides, the stability of the system has been checked by means of the velocities of the pressure waves and the relativistic adiabatic index. It is found that the configuration is stable in considering the adiabatic index criteria and is under hydrostatic balance. Finally, to mimic a realistic compact object, we have imposed the radius to be $R=9.5\ [km]$. With this information and taking different values of the parameter $A$ the total mass of the object has been determined. The resulting numerical values for the principal variables of the model established that the structure could represent a quark (strange) star mixed with dark energy., Comment: 13 pages, 5 figures. Published in EPJ C

In the present paper, we analyze the well-known 2+1 dimensional black holes (assuming a non-vanishing cosmological constant) in light of the gravitational decoupling by the minimal geometric deformation approach. To illustrate our results, we consider the BTZ geometry as the seed solution to generate new anisotropic ones. To complement the study, the curvature scalars and the energy conditions are analyzed., Comment: 8 pages, 3 figures, accepted for publication in EPJ C

The present paper is devoted to investigating the possibility of getting stellar interiors for ultra-dense compact spherical systems portraying an anisotropic matter distribution employing the gravitational decoupling by means of Minimal Geometric Deformation (MGD) procedure within the modified theory of f(R,T) gravity. According to this theory, the covariant divergence of stress-energy tensor does not vanish, hence the movement of classical particles does not follow geodesics resulting in an extra acceleration which suffices the late-time acceleration of the universe without adopting to exotic matter fields. In this regard, we have considered the algebraic function as f(R, {\rm T})= R+2\chi T, the corresponding effective stress-energy tensor is conserved as well as the exact solutions are derived, where $\chi$ indicates a coupling constant. Moreover, the physical quantities associated with the new solutions are well-behaved from the physical and mathematical point of view as well as free of geometrical singularities, violation of the causality condition, non-decreasing thermodynamic functions. Thereafter, the physical viability of the obtained model is affirmed by performing several physical tests of the main salient features such as energy density, radial, and tangential pressure, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability. On the other hand, we have generated the M-R curves from our solutions in the four different scenarios, including GR, GR+MGD, f(R,T) and f(R,T)+MGD, and we found a perfect fit for many compact spherical objects in these scenarios by changing the gravitational decoupling constant \alpha and the coupling constant \chi as free parameters. The present study reveals that the modified f(R,T) gravity through gravitational decoupling by means of MGD method is a suitable theory to explain compact stellar spherical systems...., Comment: 3 tables, 12 figures

In this work we investigate the extra packing of mass within the framework of gravitational decoupling by means of Minimal Geometric Deformation approach. It is shown that, after a suitable set of the free parameters involved, the like--Tolman IV solution extended by Minimal Geometric Deformation not only acquire extra packing of mass but it corresponds to a stable configuration according to the adiabatic index criteria. Additionally, it is shown that the extra packing condition induce a lower bound on the compactness parameter of the seed isotropic solution and a stringent restriction on the decoupling parameter.

We implement the Gravitational Decoupling through the Minimal Geometric Deformation method and explore its effect on exterior solutions by imposing a regularity condition in the Tolman--Oppenheimer--Volkoff equation of the decoupling sector. We obtain that the decoupling function can be expressed formally in terms of an integral involving the $g_{tt}$ component of the metric of the seed solution. As a particular example, we implement the method by using the Schwarzschild exterior as a seed and we obtain that the asymptotic behavior of the extended geometry corresponds to a manifold with constant curvature.

This article is devoted to the study of new exact analytical solutions in the background of Reissner-Nordstr\"{o}m space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general equation of state, relating the components of the $\theta$-sector in order to obtain the new material contributions and the decoupler function $f(r)$. Besides, we obtain the bounds on the free parameters of the extended solution to avoid new singularities. Furthermore, we show the finitude of all thermodynamic parameters of the solution such as the effective density $\tilde{\rho}$, radial $\tilde{p}_{r}$ and tangential $\tilde{p}_{t}$ pressure for different values of parameter $\alpha$ and the total electric charge $Q$. Finally, the behavior of some scalar invariants, namely the Ricci $R$ and Kretshmann $R_{\mu\nu\omega\epsilon}R^{\mu\nu\omega\epsilon}$ scalars are analyzed. It is also remarkable that, after an appropriate limit, the deformed Schwarzschild black hole solution always can be recovered., Comment: 11 pages, 3 figures

We introduce the electromagnetic-gravitational coupling in the Ho\v{r}ava-Lifshitz framework, in $3+1$ dimensions, by considering the Ho\v{r}ava-Lifshitz gravity theory in $4+1$ dimensions at the kinetic conformal point and then performing a Kaluza-Klein reduction to $3+1$ dimensions. The action of the theory is second order in time derivatives and the potential contains only higher order spacelike derivatives up to $z=4$, $z$ being the critical exponent. These terms include also higher order derivative terms of the electromagnetic field. The propagating degrees of freedom of the theory are exactly the same as in the Einstein-Maxwell theory. We obtain the Hamiltonian, the field equations and show consistency of the constraint system. The kinetic conformal point is protected from quantum corrections by a second class constraint. At low energies the theory depends on two coupling constants, $\beta$ and $\alpha$. We show that the anisotropic field equations for the gauge vector is a deviation of the covariant Maxwell equations by a term depending on $\beta-1$. Consequently, for $\beta=1$, Maxwell equations arise from the anisotropic theory at low energies. We also prove that the anisotropic electromagnetic-gravitational theory at the IR point $\beta=1$, $\alpha=0$, is exactly the Einstein-Maxwell theory in a gravitational gauge used in the ADM formulation of General Relativity.

In the present work, we investigate the possibility of obtaining stellar interiors for static self-gravitating systems describing an anisotropic matter distribution in the framework of Rastall gravity through gravitational decoupling by means of minimal geometric deformation approach. Due to Rastall gravity breaks down the minimal coupling matter principle, we have provided an exhaustive explanation about how Israel-Darmois junction conditions work in this scenario. Furthermore, to obtain the deformed space-time, the mimic constraint procedure has been used. In order to check the viability of this proposal, we have applied it to the well known Tolman IV solution. A complete thermodynamic description of the effects introduced by the additional source is given. Additionally, the results have been compared with their similes in the picture of pure general relativity, pure Rastall gravity and within the framework of general relativity including gravitational decoupling. To perform the mathematical and graphical analysis we have taken the gravitational decoupling constant $\alpha$ and the Rastall's parameter $\lambda$ as free parameters and the compactness factor describing the general relativity sector to be $0.2$. Besides, to provide a more realistic picture we have bounded both parameters $\alpha$ and $\lambda$ by using real observational data to explore the limits of the theory under this particular model. Applications to study neutron or quark stars are suggested by using this methodology., Comment: 23 pages, 5 figues

The present work is focused on the investigation of the existence of compact structures describing anisotropic matter distributions within the framework of modified gravity theories, specifically f(R,$\mathcal{T}$) gravity theory. Additionally, we have taken f(R,$\mathcal{T}$) as a linear function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as $f(R,\mathcal{T})$=$R+2\chi\mathcal{T}$,where $\chi$ is a dimensionless coupling parameter, and the Lagrangian matter $\mathcal{L}_m=-\frac{1}{3}\left(2p_{t}+p_{r}\right)$, to describe the complete set of field equations for the anisotropic matter distribution. We follow the embedding class one procedure using Eisland condition to obtain a full space-time description inside the stellar configuration. Once the space-time geometry is specified we determine the complete solution of the modified Einstein equations by using the MIT bag model equation of state $p_{r}=\frac{1}{3}\left(\rho-4B\right)$ that describes the strange quark matter (SQM) distribution inside the stellar system, where $B$ denotes a bag constant. The physical validity of our anisotropic solution is confirmed by executing several physical tests. It is worth mentioning that with the help of the observed mass values for the various strange star candidates we have predicted the exact radii by taking different values for $\chi$ and $B$. These predicted radii show monotonic decreasing nature as the parameter $\chi$ is moved from $-0.8$ to $0.8$ progressively. In this case, our anisotropic stellar system becomes more massive and transforms into more dense compact stars., Comment: Accepted in Physical Review D

This paper is devoted in the study of the hydrostatic equilibrium of stellar structure in the framework of modified $f(R, T)$ gravity theory that allows the non-conservation of energy-momentum, with possible implications for several cosmological and astrophysical issues such as the late-time cosmic acceleration of the universe without appealing to exotic matter fields. For this purpose, we consider the gravitational Lagrangian by taking an arbitrary function of the Ricci scalar and the trace of the stress-energy tensor. We obtain a generic form for the gravitational field equations and derive the field equation for $f(R,T)$ = $R+2 \chi T$. Here we propose a particular metric potential \textit{Buchdahl ansatz} [Phys. Rev. D 116, 1027 (1959)] in principle, of explaining almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source. For the choice of $f(T)= 2\chi T$ one may observe that the pressure and energy density profiles are markedly different. Important cases, which have been analyzed in detail, are all possible Buchdahl solutions for spherical equilibrium configuration in $f(R, T)$ gravity and compare them with standard gravity theory. We find that Buchdahl's solution in Einstein gravity and $f(R,T)$ gravity behaves in a similar manner but in some situations Einstein gravity displays more pleasing behavior than its $f(R,T)$ counterpart., Comment: 16 figures and 4 tables

The main aim of this paper is to obtain analytic relativistic anisotropic spherical solutions in f(R,$\mathcal{T}$) scenario. To do so we use modified Durgapal-Fuloria metric potential and the isotropic condition is imposed in order to obtain the effective anisotropic factor $\tilde{\Delta}$. Besides, a notable and viable election on f(R,$\mathcal{T}$) gravity formulation is taken. Specifically $f(R,\mathcal{T})=R+2\chi\mathcal{T}$, where $R$ is the Ricci scalar, $\mathcal{T}$ the trace of the energy-momentum tensor and $\chi$ a dimensionless parameter. This choice of $f(R,\mathcal{T})$ function modifies the matter sector only, including new ingredients to the physical parameters that characterize the model such as density, radial, and tangential pressure. Moreover, other important quantities are affected such as subliminal speeds of the pressure waves in both radial and transverse direction, observational parameters, for example, the surface redshift which is related with the total mass $M$ and the radius $r_{s}$ of the compact object. Also, a transcendent mechanism like equilibrium through generalized Tolman-Oppenheimer-Volkoff equation and stability of the system are upset. We analyze all the physical and mathematical general requirements of the configuration taking $M=1.04 M_{\odot}$ and varying $\chi$ from $-0.1$ to $0.1$. It is shown by the graphical procedure that $\chi<0$ yields to a more compact object in comparison when $\chi\geq0$ (where $\chi=0.0$ corresponds to general relativity theory) and increases the value of the surface redshift. However, negative values of $\chi$ introduce in the system an attractive anisotropic force (inward) and the configuration is completely unstable (corroborated employing Abreu's criterion). Furthermore, the model in Einstein gravity theory presents cracking while for $\chi>0$ the system is fully stable.

This article is devoted to the study of high dense charged anisotropic compact structures in the framework of $f(R,\mathcal{T})$ gravity theory. The principal aims of this investigation, regard the extension of the isotropic Durgapal-Fuloria model within the context of charged isotropic $f(R,\mathcal{T})$ solutions. The second main goal of this work is to apply the gravitational decoupling via a minimal geometric deformation (MGD) scheme in $f(R,\mathcal{T})$ gravity. Finally, the third one is to derive an anisotropic version of the charged isotropic model previously obtained by applying gravitational decoupling technology. This MGD approach splits the system of equations into two separate sets, one corresponding with the f(R,$\mathcal{T}$) gravity system and another corresponding to the anisotropic sector governed by the extra source $\theta_{\mu\nu}$.To address this task we have considered some ingredients: I) the f(R,$\mathcal{T}$) model corresponds to a linear functional of the Ricci's scalar and the trace of the energy-momentum tensor $\mathcal{T}$, specifically $ f(R,\mathcal{T}) =R+2\chi\mathcal{T}$, being $\chi$ a running coupling constant. II) The matter distribution is taken to be an isotropic fluid one, III) the Lagrangian matter $\mathcal{L}_{m}$ corresponds to the negative isotropic pressure \i.e, $-p$ and IV) in order to solve the $\theta$-sector, a suitable form for the decoupler function $f(r)$ has been imposed, respecting all the physical and mathematical requirements. Finally, to check and contrast our model an exhaustive mathematical, physical and graphical analysis is performed in order to show all the properties that characterize the compact structure. It is worth mentioning that when $\chi=0$ Einstein's gravity theory results are recovered., Comment: 18 figures, submitted in JCAP

The present work is devoted to the study of anisotropic compact matter distributions within the framework of 5-dimensional Einstein-Gauss-Bonnet gravity. To solve the field equations, we have considered that the inner geometry is described by Tolman-Kuchowicz spacetime. The Gauss-Bonnet Lagrangian is coupled to Einstein-Hilbert action through a coupling constant. When this coupling tends to zero general relativity results are recovered. We analyze the effect of this parameter on the principal salient features of the model, such as energy density, radial and tangential pressure and anisotropy factor.Additionally, the behaviour of the subliminal sound speed of the pressure waves in the principal direction of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing causality condition and energy conditions, respectively. All these subjects are supported by mean of physical, mathematical and graphical survey

In the present article, we discuss relativistic anisotropic solutions of the Einstein field equation for the spherically symmetric line element under the class I condition. To do so we apply the embedding class one technique using Eisland condition. Within this approach, one arrives at a particular differential equation that links the two metric components $e^{\nu}$ and $e^{\lambda}$. In order to obtain the full space-time description inside the stellar configuration we ansatz the generalized form of metric component $g_{rr}$ corresponding to the Finch-Skea solution. Once the space-time geometry is specified we obtain the complete thermodynamic description i.e. the matter density $\rho$, the radial, and tangential pressures $p_r$ and $p_t$, respectively. Graphical analysis shows that the obtained model respects the physical and mathematical requirements that all ultra-high dense collapsed structures must obey. The $M-R$ diagram suggests that the solution yields stiffer EoS as parameter $n$ increases. The $M-I$ graph is in agreement with the concepts of Bejgar et al. \cite{bej} that the mass at $I_{max}$ is lesser by few percent (for this solution $\sim 3\%$) from $M_{max}$. This suggests that the EoSs is without any strong high-density softening due to hyperonization or phase transition to an exotic state., Comment: 14 figures, Accepted in European Physical Journal C

In this work we obtain an analytic and well behaved solution to Einstein's field equations describing anisotropic matter distribution. It's achieved in the embedding class one spacetime framework using Karmarkar's condition. We ansatz the metric potential $g_{tt}$ corresponding to Wyman IIa solution. The obtained model is representing some strange star candidates such as Cen X-3, LMC X-4 and 4U 1538-52. A graphical analysis shows that our model is free from physical and geometric singularities and satisfies all the physical admissibility conditions from the physical and mathematical point of view., Comment: arXiv admin note: substantial text overlap with arXiv:1808.01699

Durgapal's fifth isotropic solution describing spherically symmetric and static matter distribution is extended to an anisotropic scenario. To do so we employ the gravitational decoupling through the minimal geometric deformation scheme. This approach allows to split Einstein's field equations in two simply set of equations, one corresponding to the isotropic sector and other to the anisotropic sector described by an extra gravitational source. The isotropic sector is solved by the Dugarpal's model and the anisotropic sector is solved once a suitable election on the minimal geometric deformation is imposes. The obtained model is representing some strange stars candidates and fulfill all the requirements in order to be a well behaved physical solution to the Einstein's field equations.

We analyze the electromagnetic-gravity interaction in a pure Ho\v{r}ava-Lifshitz framework. To do so we formulate the Ho\v{r}ava-Lifshitz gravity in $4+1$ dimensions and perform a Kaluza-Klein reduction to $3+1$ dimensions. We use this reduction as a mathematical procedure to obtain the $3+1$ coupled theory, which at the end is considered as a fundamental, self-consistent, theory. The critical value of the dimensionless coupling constant in the kinetic term of the action is $\lambda=1/4$. It is the kinetic conformal point for the non-relativistic electromagnetic-gravity interaction. In distinction, the corresponding kinetic conformal value for pure Ho\v{r}ava-Lifshitz gravity in $3+1$ dimensions is $\lambda=1/3$. We analyze the geometrical structure of the critical and noncritical cases, they correspond to different theories. The physical degrees of freedom propagated by the noncritical theory are the transverse traceless graviton, the transverse gauge vector and two scalar fields. In the critical theory one of the scalars is absent, only the dilaton scalar field is present. The gravity and vector excitations propagate with the same speed, which at low energy can be taken to be the speed of light. The field equations for the gauge vector in the non-relativistic theory have exactly the same form as the relativistic electromagnetic field equations arising from the Kaluza-Klein reduction of General Relativity, and are equal to them for a particular value of one of the coupling constants. The potential in the Hamiltonian is a polynomial of finite degree in the gauge vector and its covariant derivatives.

In the present article, we have constructed a static charged anisotropic compact star model of Einstein field equations for a spherically symmetric space-time geometry. Specifically, we have extended the charged isotropic Heintzmann solution to an anisotropic domain. To address this work, we have employed the gravitational decoupling through the so called minimal geometric deformation approach. The charged anisotropic model is representing the realistic compact objects such as $RXJ1856-37$ and $SAX J1808.4-3658(SS2)$. We have reported our results in details for the compact star $RXJ1856-37$ on the ground of physical properties such as pressure, density, velocity of sound, energy conditions, stability conditions, Tolman-Oppenheimer-Volkoff equation and redshift etc.

This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric Deformation (MGD). For this we apply MGD to Heintzmann's solution obtaining two new analytic and well behaved anisotropic solutions, in which all their parameters such as the effective density, the effective radial and tangential pressure, as well as radial and tangential sound speed, fulfill each of the requirements for the physical acceptability available in the literature.