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
The main objective of this work is to study in some detail the Randall-Sundrum gravity under the gravitational decoupling through the minimal geometric deformation approach (MGD-decoupling). We show a family of new black hole solutions as well as new exact interior solutions for self-gravitating stellar systems and we discuss the corresponding matching conditions.
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.
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.
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 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.
In this work we construct an ultracompact star configuration in the framework of Gravitational Decoupling by the Minimal Geometric Deformation approach. We use the complexity factor as a complementary condition to close the system of differential equations. It is shown that for a polynomial complexity the resulting solution can be matched with two different modified-vacuum geometries.
In this work we develop a simple protocol to construct interior solutions through Gravitational Decoupling by the Minimal Geometric Deformation extended satisfying the vanishing complexity condition. The method is illustrated by using Tolman VII and Tolman IV solutions as isotropic seeds.
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.
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.
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.
Two different forms of time dilation, namely, the kinematical time dilation of special relativity and gravitational red shift are coupled during observations of systems moving through a gravitational field. In the particular situation of free fall in a Schwarzschild geometry these two effects are decoupled and in consequence the time dilation, as observed by a distant observer, factorises. Such a factorization is not a universal feature. We define here a necessary and sufficient criterion for time dilation and gravitational red-shift decoupling. This property is manifested in a particular form…
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.
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…
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 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.
In this work we study the 2+1 Einstein-Klein-Gordon system in the framework of Gravitational Decoupling. We associate the generic matter decoupling sector with a real scalar field so we can obtain a constraint which allows to close the system of differential equations. The constraint corresponds to a differential equation involving the decoupling functions and the metric of the seed sector and will be independent of the scalar field itself. We show that when the equation admits analytical solutions, the scalar field and the self-interacting potential can be obtained straightforwardly. We found…
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 …
In this paper we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution which can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and well-known when the mass function is the function only of space coordinate $r$. The second case is Vaidya spacetime case when the mass function depends on time $v$ . And the third case represents the generalization of these two cases: the mass function is the function of both $r$ and $v$. We also calculate the apparent horizon and singularity location f…
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, …
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 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…
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…
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…
We provide an algorithm that shows how to decouple gravitational sources in Pure Lovelock gravity. This method allows to obtain several new and known analytic solutions of physical interest in scenarios with extra dimensions and with presence of higher curvature terms. Furthermore, using our method, it is shown that applying the minimal geometric deformation to the Anti de Sitter space time it is possible to obtain regular black hole solutions.
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…
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…
We provide a way of decoupling the first law of thermodynamics in two sectors : the standard first law of thermodynamics and the quasi first law of thermodynamics. It is showed that both sectors share the same thermodynamics volume and the same entropy. However, the total thermodynamics pressure, the total temperature and the total local energy correspond to a simple sum of the thermodynamics contributions of each sector. Furthermore, it is showed a simple example, where there is a phase transition due to the behavior of the temperature at the quasi sector.
We introduce a systematic and direct procedure to generate hairy rotating black holes by deforming a spherically symmetric seed solution. We develop our analysis in the context of the gravitational decoupling approach, without resorting to the Newman-Janis algorithm. As examples of possible applications, we investigate how the Kerr black hole solution is modified by a surrounding fluid with conserved energy-momentum tensor. We find non-trivial extensions of the Kerr and Kerr-Newman black holes with primary hair. We prove that a rotating and charged black hole can have the same horizon as Kerr'…
Gravitational decoupling can add hair to the black holes by adding extra sources. The quasinormal modes of hairy black hole caused by gravitational decoupling for the massless scalar field, electromagnetic field, and gravitational perturbation are investigated. The equations of effective potential for three perturbations are derived in hairy black hole spacetime. We also study the time evolution corresponding to the three perturbations, and the quasinormal mode frequencies are calculated using the Prony method through the time-domain profiles. By analyzing the influence of the hairs ($α$, $l_0…
Nonsingular hairy black holes by gravitational decoupling
College of Physics Science and Technology, Hebei University（河北大学物理科学与工程学院）；Hebei Key Lab of Optic-Electronic Information and Materials, Hebei University（河北大学河北省光电信息与材料重点实验室）；National-Local Joint Engineering Laboratory of New Energy Photoelectric Devices, Hebei University（河北大学新能源光电器件国家地方联合工程实验室）；Key Laboratory of High-pricision Computation and Application of Quantum Field Theory of Hebei Province, Hebei University（河北大学量子场论高精度计算与应用重点实验室）
Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric Deformation approach to study extensions of the theory of General Relativity in a cosmological context. This is possible since such approach allows the decoupling of gravitational sources, and the Einstein field equations can be analytically solved with the presence of a new gravitational sector once a known GR solution is considered. In particular, we implement such …
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…
Hairy black holes in the gravitational decoupling setup are studied from the perspective of conformal anomalies. Fluctuations of decoupled sources can be computed by measuring the way the trace anomaly-to-holographic Weyl anomaly ratio differs from unit. Therefore the gravitational decoupling parameter governing three hairy black hole metrics is then bounded to a range wherein one can reliably emulate AdS/CFT with gravitational decoupled solutions, in the tensor vacuum regime.
Gravitational decoupled compact polytropic hybrid stars are here addressed in generalized Horndeski scalar-tensor gravity. Additional physical properties of hybrid stars are scrutinized and discussed in the gravitational decoupling setup. The asymptotic value of the mass function, the compactness, and the effective radius of gravitational decoupled hybrid stars are studied for both cases of a bosonic and a fermionic prevalent core. These quantities are presented and discussed as functions of Horndeski parameters, the decoupling parameter, the adiabatic index, and the polytropic constant. Impor…
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…
Black holes with hair represented by generic fields surrounding the central source of the vacuum Schwarzschild metric are examined under the minimal set of requirements consisting of i) the existence of a well defined event horizon and ii) the strong or dominant energy condition for the hair outside the horizon. We develop our analysis by means of the gravitational decoupling approach. We find that trivial deformations of the seed Schwarzschild vacuum preserve the energy conditions and provide a new mechanism to evade the no-hair theorem based on a primary hair associated with the charge gener…
We show how to decoupling two spherically symmetric and static gravitational sources through the most general possible extension of the so-called Minimal Geometric Deformation-decoupling. As a test, we decouple the Einstein-Maxwell system and reproduce the Reissner-Nordstrom black hole solution. We show the potential of this method to study i) the consequences of modified gravity on general relativity, ii) to investigate the conjectured dark matter, and iii) to study hairy black holes.
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…
We analyze the effective field equations of the Randall-Sundrum braneworld coupled with a Klein-Gordon scalar field through the minimal geometric deformation decoupling method (MGD-decoupling). We introduce two different ways to apply the MGD-decoupling method to obtain new solutions for this enlarged system. We also compare the behavior of the new solutions with those obtained directly from the Randall-Sumdrum braneworld without coupling to the scalar field.
This paper considers gauge-invariant and covariant gravitational perturbations on arbitrary vacuum locally rotationally symmetric (LRS) class II space-times. Ultimately, we derive four decoupled equations governing four specific combinations of the gravito-electromagnetic (GEM) 2-tensor harmonic amplitudes. We use the gauge-invariant and covariant 1+1+2 formalism which Clarkson and Barrett developed for analysis of vacuum Schwarzschild perturbations. In particular we focus on the first-order 1+1+2 GEM system and use linear algebra techniques suitable for exploiting its structure. Consequently,…
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…
We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b) generate new solutions for self-gravitating distributions with the same or vanishing complexity factor. A few working examples are given for illustrative purposes.
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.
Echoes of a hairy black hole from gravitational decoupling
Guizhou University of Finance and Economics（贵州财经大学）；Eastern Mediterranean University（东地中海大学）；Universit degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Salerno - Sezione di Napoli（意大利国家核物理研究所 - 萨莱诺协作组 - 那不勒斯分部）；Guizhou Minzu University（贵州民族大学）；Guizhou University（贵州大学）
The gravitational decoupling is applied to studying minimal geometric deformed (MGD) compact superfluid stars, in covariant logarithmic scalar gravity on fluid branes. The brane finite tension is shown to provide more realistic values for the asymptotic value of the mass function of MGD superfluid stars, besides constraining the range of the self-interacting scalar field, minimally coupled to gravity. Several other physical features of MGD superfluid stars, regulated by the finite brane tension and a decoupling parameter, are derived and discussed, with important corrections to the general-rel…
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 propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renormalization mass scale $μ$. The new predicted running for the gravitational couplings are fully consistent with decoupling of heavy massive fields. This is a somewhat improvement with respect to the more standard treatment of minimal (DeWitt-Schwinger) subtractions via dimensional regularization. We also show how the vacuum metamorphosis model emerges from the running couplings.
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…
