This paper is devoted to evaluating exact anisotropic spherical solutions for static self-gravitating systems through extended geometric deformation decoupling technique. For this purpose, we consider an isotropic Tolman IV solution and extend it to anisotropic domain by transforming both temporal as well as radial metric potentials. To examine the physical viability and stability of interior anisotropic solutions, we plot energy bounds, TOV equation, causality condition and adiabatic index for the stars Her X-I and PSR J 1416-2230. It is found that both obtained models show realistic behavior as they fulfill all physical constraints as well as stability criterion. We conclude that the extended gravitational decoupling approach provides more proficient results to discuss the interior configuration of stellar structures.
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.
In this paper, we consider well known Tolman V perfect fluid solution and extend it to its an anisotropic version using gravitational decoupling by minimal geometric deformation approach and analyze the behavior of new version of the solution graphically. The effects of coupling constant on anisotropic factor has been measured and presented graphically. The matching conditions at the surface of inner and outer geometry have also been discussed. The viability of the solution has been studied by presenting the physical analysis of the solution.
Using the gravitational decoupling by the minimal geometric deformation approach, we build an anisotropic version of the well-known Tolman VII solution, determining an exact and physically acceptable interior two-fluid solution that can represent behavior of compact objects. Comparison of the effective density and density of the perfect fluid is demonstrated explicitly. We show that the radial and tangential pressure are different in magnitude giving thus the anisotropy of the modified Tolman VII solution. The dependence of the anisotropy on the coupling constant is also shown.
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…
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 …
We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the star surface with the outer Schwarzschild space-time are studied in great details, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic…
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 deformati…
In this work we will analyse the complexity factor, proposed by L. Herrera, for spherically symmetric static matter distributions satisfying a polytropic equation through the gravitational decoupling method. Specifically, we will use the 2-step GD, which is a particular case of the extended geometric deformation (EGD), to obtain analytic polytropic solutions of Einstein's equations. In order to give an example, we construct a model satisfying a polytropic equation of state using Tolman IV as a seed solution.
In this work we obtain an anisotropic neutron star solution by gravitational decoupling starting from a perfect fluid configuration which has been used to model the compact object PSR J0348+0432. Additionally, we consider the same solution to model the Binary Pulsar SAX J1808.4-3658 and X-ray Binaries Her X-1 and Cen X-3 ones. We study the acceptability conditions and obtain that the MGD--deformed solution obey the same physical requirements as its isotropic counterpart. Finally, we conclude that the most stable solutions, according to the adiabatic index and gravitational cracking criterion, …
We study the minimal geometric deformation decoupling in $2+1$ dimensional space--times and implement it as a tool for obtaining anisotropic solutions from isotropic geometries. Interestingly, both the isotropic and the anisotropic sector fulfill Einstein field equations in contrast to the cases studied in $3+1$ dimensions. In particular, new anisotropic solutions are obtained from the well known static BTZ solution.
The aim of this work is to obtain new analitical solutions for Einstein equations in the anisotropical domain. This will be done via the minimal geometric deformation (MGD) approach, which is a simple and systematical method that allow us to decouple the Einstein equations. It requires a perfect fluid known solution that we will choose to be Finch-Skeas(FS) solution. Two different constraints were applied, and in each case we found an interval of values for the free parameters, where necesarly other physical solutions shall live.
In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of the fact that Gravitational Decoupling allows to decrease the number of degrees of freedom once a well known solution of the Einstein field equations is provided as a seed so after demanding the polytropic equation for the radial pressure the system is automatically closed. The approach not only allows to extend both isotropic or anisotropic known solutions but simplifies the computation of the Tolman mass whenever the Minimal Geometric Deformation is con…
In this work we implement the Minimal Geometric Deformation decoupling method to obtain general static interior solutions for a BTZ vacuum from the most general isotropic solution in $2+1$ dimensions including the cosmological constant $Λ$. We obtain that the general solution can be generated only by the energy density of the original isotropic sector, so that this quantity plays the role of a generating function. Although as a particular example we study the static star with constant density, the method here developed can be easily applied to more complex situations described by other energy …
In this work we construct a static and spherically symmetric black hole geometry supported by a family of generic mono-parametric sources thorough the Gravitational Decoupling. The parameter characterizing the matter sector can be interpreted as hair which cannot be associated to any global charge. Although the solution is constructed by demanding the weak energy condition, we find that the resulting matter sector satisfies all the energy conditions at and outside the horizon. We study the effect of the hair on the periastron advance and the gravitational lensing of the black hole. We estimate…
By using the gravitational decoupling through the minimal geometric deformation approach (MGD-decoupling), we show a simple and powerful method to generate physically acceptable exact analytical solutions for anisotropic stellar distributions in general relativity. We find that some perfect fluid configurations could be incompatible with anisotropic effects produced by scalar fields.
In this article, we propose a physical condition to extend interior isotropic solutions to anisotropic domains by gravitational decoupling in the framework of the Minimal Geometric Deformation approach. In particular, it is found that by using an expression reminiscent of the classical anisotropy factor, we can close the decoupling system of equations and a new anisotropic solution can be found. As an example, we extend the well--known Tolman IV.
We show the first simple, systematic and direct approach to decoupling gravitational sources in general relativity. As a direct application, a robust and simple way to generate anisotropic solutions for self-gravitating systems from perfect fluid solutions is presented.
This paper investigates the behavior of anisotropic static spheres that are constructed by employing a minimal geometric deformation in the framework of $f(R,T^{2})$ gravity ($T^{2}=T_{ζν}T^{ζν}$, $R$ is the Ricci scalar and $T_{ζν}$ is the energy-momentum tensor). We consider a spherical setup with two sources: seed and additional. It is assumed that the seed source is isotropic whereas the new source is responsible for inducing anisotropy. We deform the $g_{rr}$ component to split the field equations into two sets. The first array corresponds to the isotropic solution whereas the second set …
We employ the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling) in order to generate an exact anisotropic and non-uniform version of the ultracompact Schwarzschild star, or 'gravastar', proposed by Mazur and Mottola. This new system represents an ultracompact configuration of radius $R_{S}=2\cal{M}$ whose interior metric can be matched smoothly to a conformally deformed Schwarzschild exterior. Remarkably, the model satisfies some of the basic requirements to describe a stable stellar model, such as a positive density everywhere and decreasing monotonously from…
In this work, we have adopted gravitational decoupling by Minimal Geometric Deformation (MGD) approach and have developed an anisotropic version of well-known Tolman VII isotropic solution in the framework of $f(R, T)$ gravity, where $R$ is Ricci scalar and $T$ is trace of energy momentum tensor. The set of field equations has been developed with respect to total energy momentum tensor, which combines effective energy momentum tensor in $f(R,T)$ gravity and additional source $ϕ_{ij}$. Following MGD approach, the set of field equations has been separated into two sections. One section represent…
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 gravi…
The current theoretical development identified as the gravitational decoupling via Complete Geometric Deformation (CGD) method that has been introduced to explore the nonmetricity $Q$ effects in relativistic astrophysics. In the present work, we have investigated the gravitationally decoupled anisotropic solutions for the strange star in the framework of $f(Q)$ gravity by utilizing the CGD technique. To do this, we started with Tolman metric ansatz along with the MIT Bag model equation of state related to the hadronic matter. The solutions of the governing equations of motions are obtained by …
The purpose of this paper is to obtain exact solutions for charged anisotropic spherically symmetric matter configuration. For this purpose, we consider known solution for isotropic spherical system in the presence of electromagnetic field and extend it to two types of anisotropic charged solutions through gravitational decoupling approach. We examine physical characteristics of the resulting models. It is found that only first solution is physically acceptable as it meets all the energy bounds as well as stability criterion. We conclude that stability of the first model is enhanced with the i…
In this paper, we consider static spherical structure to develop some anisotropic solutions by employing the extended gravitational decoupling scheme in the background of $f(\mathcal{R},\mathcal{T},\mathcal{R}_{γχ}\mathcal{T}^{γχ})$ gravity, where $\mathcal{R}$ and $\mathcal{T}$ indicate the Ricci scalar and trace of the energy-momentum tensor, respectively. We transform both radial as well as temporal metric functions and apply them on the field equations that produce two different sets corresponding to the decoupling parameter $ξ$. The first set is associated with isotropic distribution, i.e…
We provide a higher dimensional extension of the gravitational decoupling method. This extended method allows to obtain new analytic and well behaved solutions that could be associated to higher dimensional stellar distributions. Furthermore, we find a new five dimensional anisotropic and well behaved analytical solution.
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 …
In this paper, we construct anisotropic spherical solutions from known isotropic solutions through extended gravitational decoupling method in the background of self-interacting Brans-Dicke theory. The field equations are decoupled into two sets by applying geometric deformations on radial as well as temporal metric components. The first array corresponds to isotropic fluid while influence of the anisotropic source is confined to the second set. The isotropic sector is determined through metric functions of isotropic solutions (Tolman IV/Krori-Barua) whereas two constraints on the anisotropic …
A class of spherical collapsing exact solutions with electromagnetic charge is derived. This class of solutions -- in general anisotropic -- contains however as a particular case the charged dust model already known in literature. Under some regularity assumptions that in the uncharged case give rise to naked singularities, it is shown that the process of shell focusing singularities avoidance -- already known for the dust collapse -- also takes place here, determing shell crossing effects or a completely regular solution.
This manuscript is devoted to study the combined effect of a viable model, f(R) = R + αR^n, and electromagnetic field on the instability range of gravitational collapse. We assume charged anisotropic fluid that dissipate energy via heat flow and discuss that electromagnetic field, density inhomogeneity, shear and phase transition on astrophysical bodies can be incorporated by locally anisotropic background. Dynamical equations help to investigate the evolution of self-gravitating objects and leads to the conclusion that adiabatic index depend upon the electromagnetic background, mass and radiu…
We employ the minimal geometric deformation approach to gravitational decoupling (MGD- decoupling) in order to build an exact anisotropic version of the Schwarzschild interior solution in a space-time with cosmological constant. Contrary to the well-known Schwarzschild interior, the matter density in the new solution is not uniform and possesses subluminal sound speed. It therefore satisfies all standard physical requirements for a candidate astrophysical object.
The objective of this paper is to discuss anisotropic solutions representing static spherical self-gravitating systems in $f(R)$ theory. We employ the extended gravitational decoupling approach and transform temporal as well as radial metric potentials which decomposes the system of non-linear field equations into two arrays: one set corresponding to seed source and the other one involves additional source terms. The domain of the isotropic solution is extended in the background of $f(R)$ Starobinsky model by employing the metric potentials of Krori-Barua spacetime. We determine two anisotropi…
In this work we extend the so--called Minimal Geometric Deformation method in $2+1$ dimensional space--times with cosmological constant in order to deal with the gravitational decoupling of two circularly symmetric sources. We find that, even though the system here studied is lower dimensional and it includes the cosmological constant, the conditions for gravitational decoupling of two circularly symmetric sources coincides with those found in the $3+1$ dimensional case. We obtain that, under certain circumstances, the extended gravitational decoupling leads to the decoupling of the sources in…
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The solution obtained has the characteristics that the pressure and the cosmological parameter vanish at the centre and at the boundary with a maximum value somewhere inside the body. It has been argued that a variable $ Λ$ is as much important physically in Astrophysics as in Cosmology.
In this work we implement the Minimal Geometric Deformation method to obtain the isotropic sector and the decoupler matter content of any anisotropic solution of the Einstein field equations with cosmological constant in $2+1$ dimensional space--times. We obtain that the solutions of both sectors can be expressed analytically in terms of the metric functions of the original anisotropic solutions instead of formal integral as in its $3+1$ counterpart. As a particular example we study a regular black hole solution and we show that, depending on the sign of the cosmological constant, the solution…
We investigate how a spherically symmetric fluid modifies the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the fluid and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling realised via the minimal geometric deformation approach, which allows us to prove that the fluid must be anisotropic. Several cases are then explicitly shown
We use gravitational decoupling to establish a connection between the minimal geometric deformation approach and the standard method for obtaining anisotropic fluid solutions. Motivated by the relations that appear in the framework of minimal geometric deformation, we give an anisotropy factor that allows us to solve the quasi--Einstein equations associated to the decoupler sector. We illustrate this by building an anisotropic extension of the well known Tolman IV solution, providing in this way an exact and physically acceptable solution that represents the behavior of compact objects. We sho…
In this work we analyse the stability of self gravitating spheres in the context of gravitational cracking. Besides exploring the role played by the anisotropy in the occurrence of cracking, we also study the effect of the complexity factor recently introduced by L. Herrera in Phys. Rev. D 97, 044010 (2018). The models under study correspond to anisotropic solutions obtained in the framework of the Gravitational Decoupling. The effect that the variation of the decoupling parameter and the compactness of the source have on the behaviour of the radial force is studied in detail.
In this study, the gravitational decoupling approach via extended geometric deformation is utilized to generate analytical black hole solutions owing to its simplicity and effectiveness. Considering the external fields surrounding Schwarzschild AdS black holes, we derive hairy black hole solutions in asymptotic AdS spacetime, satisfying the strong and dominant energy conditions. Moreover, we find that if the black hole spacetime is a fluid system, the fluid under each of these conditions is anisotropic.
This paper develops some new analytical solutions to the $f(\mathbb{R},\mathbb{T})$ field equations through extended gravitational decoupling. For this purpose, we take spherical anisotropic configuration as a seed source and extend it to an additional source. The modified field equations comprise the impact of both sources which are then decoupled into two distinct sets by applying the transformations on $g_{tt}$ and $g_{rr}$ metric potentials. The original anisotropic source is adorned by the first sector, and we make it solvable by considering two different well-behaved solutions. The secon…
In this paper, we develop two anisotropic solutions for static self-gravitating spherical structure in the presence of electromagnetic field through gravitational decoupling approach in $f(G,T)$ theory, where $G$ and $T$ denote the Gauss-Bonnet term and trace of the energy-momentum tensor, respectively. The extra source with isotropic seed sector is responsible for generating anisotropy in the spacetime. The system of field equations is decoupled into two arrays by using minimal geometric deformation in the radial component. The first set portrays the isotropic regime whereas the second set re…
We investigate how a spherically symmetric scalar field can modify the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the scalar field and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling by Minimal Geometric Deformation (MGD-decoupling), which allows us to show that, under the MGD paradigm, the Schwarzschild solution is modified in such a way that a naked singularity appears.
Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, tau, experienced by the dust particles. The general solution contains four arbitrary functions of R - M(R), L(R), E(R) and r(0,R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemaitre-Tolman-Bondi solution. We present a discussion of the types of solution, and some examp…
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 exoti…
In the present paper, we discuss the role of gravitational decoupling to isotropize the anisotropic solution of Einstein's field equations in the context of the complete geometric deformation (CGD) approach and its influence on the complexity factor introduced by L. Herrera (Phys. Rev. D 97, 044010 (2018)) in the static self-gravitating system. Moreover, we also proposed a simple and effective technique to generate new solutions for self-gravitating objects via CGD approach by using two systems with the same complexity factor and vanishing complexity factor proposed by Casadio et al. Eur. Phys…
We study quasi-spherical Szekeres space-time (which possess no killing vectors) for perfect fluid, matter with tangential stress only and matter with anisotropic pressure respectively. In the first two cases cosmological solutions have been obtained and their asymptotic behaviour have been examined while for anisotropic pressure, gravitational collapse has been studied and the role of the pressure has been discussed.
In this paper, we consider static self-gravitating spherical spacetime and determine various anisotropic solutions through the extended gravitational decoupling technique in $f(\mathcal{R},\mathcal{T},\mathcal{R}_{λξ}\mathcal{T}^{λξ})$ gravity to analyze the influence of electromagnetic field on them. We construct two different sets of modified field equations by employing the transformations on both radial as well as temporal metric potentials. The first set symbolizes the isotropic fluid distribution, thus we take Krori-Barua solution to deal with it. The indefinite second sector comprises t…
