Minimal Geometric Deformation Approach Research Articles

Charged anisotropic compact stellar models under gravitational decoupling scheme

The aim of this paper is to obtain new physically admissible exact anisotropic stellar models via gravitational decoupling technique. This will be done by taking Korkina and Orlyanskii model solution as a seed solution and extend it to an anisotropic domain via gravitational decoupling through the minimal geometric deformation (MGD) approach. We analyze the physical properties of four compact star models Her [Formula: see text] (Mass [Formula: see text], [Formula: see text][Formula: see text]km), LMC [Formula: see text] ([Formula: see text], [Formula: see text][Formula: see text]km), PSR [Formula: see text] ([Formula: see text], [Formula: see text][Formula: see text]km) and PSR [Formula: see text] ([Formula: see text], [Formula: see text][Formula: see text]km). We demonstrate the stability conditions of the obtained solution by plotting energy conditions, velocity of sound, adiabatic index and all the thermodynamic parameters and equilibrium conditions via TOV equation, etc. We found that the results are physically well behaved and also fulfill the requirement of stability criteria inside the anisotropic fluid sphere. We study the physical features of the solutions in detail, analytically and graphically for the four compact stars Her [Formula: see text], LMC [Formula: see text], PSR [Formula: see text] and PSR [Formula: see text]. Based on the results we realized that the extended gravitational decoupling technique is very effective for the analysis of the interior of the compact stellar structures.

Analytical approximate solutions of AdS black holes in Einstein-Weyl-scalar gravity* *M. Z. is supported by the Natural Science Basic Research Program of Shaanxi, China (2023-JC-QN-0053). D. C. Z is supported by the Natural Science Foundation of China (12365009) and the Natural Science Foundation of Jiangxi Province, China (20232BAB201039)

We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime. Using the minimal geometric deformation (MGD) approach, we split the highly nonlinear coupled field equations into two subsystems that describe the background geometry and scalar field source, respectively. By considering the Schwarzschild-AdS metric as background geometry, we derive analytical approximate solutions of the scalar field and deformation metric functions using the homotopy analysis method (HAM), providing their analytical approximations to fourth order. Moreover, we discuss the accuracy of the analytical approximations, showing they are sufficiently accurate throughout the exterior spacetime.

Gravitationally decoupled non-Schwarzschild black holes and wormhole space–times

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.

Minimally Deformed Wormholes Inspired by Noncommutative Geometry

AbstractIn 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 α 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 an exotic matter distribution. 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.

Charged compact objects by e–MGD approach

In this work, we analyze the incidence of gravitational decoupling through the extended minimal geometric deformation (e–MGD) approach in the framework of f(R, T) gravity theory, applying it on a spherically symmetric and static charged isotropic matter distribution. Specifically, the well–known Krori–Barua toy model is translated to an anisotropic domain by deforming the complete space–time. To do so, the so–called θ–sector has been solved by using the mimic constraint for the radial pressure and a general equation of state relating the components of the θ μ ν source. A thoroughly study on the main salient features of the output such as density, radial pressure, transverse pressure and anisotropy factor is performed to check the feasibility of the model, in order to determine whether this structure can represent real celestial bodies such as neutron stars. Furthermore, the consequences of e–MGD on some relevant astrophysical parameters, that is, the total mass M, gravitational redshift z and time dilation d τ around the object are explored. It is found that the maximum mass provided by this toy model is M = 2.506M ⊙, corresponding to the massive neutron stars.

Stable stellar configurations with polynomial complexity factor

In this article, we present two new families of anisotropic solutions for static spherically symmetric stellar systems by taking into account the implications of complexity factor proposed by Herrera (Phys. Rev. D 97:044010, 2018) in the framework of gravitational decoupling. We start by taking minimal geometric deformation approach as a useful solution generating tool for the new physically viable models of anisotropic matter distributions, and utilize the Durgapal IV and Durgapal V perfect fluid stellar models as seed solutions in the mechanism under consideration. We consider a complexity factor which corresponds to a polynomial of order N, and use it as an axillary condition in order to determine the deformation function. We explore the scenarios, in which polynomial type complexity factors leads to stable stellar configurations. In all cases, both solutions produce similar results with an inappreciable changes in their magnitudes.

Vaidya-Tikekar type anisotropic fluid model by gravitational decoupling

In this paper, a new interior solution for compact objects has been obtained using the minimal geometric deformation (MGD) approach along with the embedding Class I condition. Using MGD, the original system gets split into two parts, one of them is called the Einstein system and another one is the quasi-Einstein system for the extra source The Einstein system is solved by using the Vaidya-Tikekar metric along with the Class I condition, while for the quasi-Einstein system, the mimic approach for density constraint has been used such that A detailed physical analysis has been done as well as the physical viability of the model in terms of the thermodynamical variables, and different stability factors are also tested. Furthermore, the mass-radius ratio is also calculated for 12 different stars for different values of the decoupling constant which determines how the gravitational decoupling influences the compactness.

Minimally deformed charged stellar model by gravitational decoupling in 5D Einstein–Gauss–Bonnet gravity

We investigate the possibility of existing a class of compact charged spheres made of a charged perfect fluid in the framework of Einstein–Gauss–Bonnet theory in five-dimensional spacetime (5D EGB). In order to study spherically symmetric compact stars in EGB gravity, we prefer to apply a systematic and direct approach to decoupling gravitational sources via the minimal geometric deformation approach (MGD), which allows us to prove that the fluid must be anisotropic. In fact, we specify a well-known Krori–Barua spacetime in the MGD approach that helps us to determine the decoupling sector completely. Indeed, by using this approach, we found an exact and physically acceptable solution which satisfies all the elementary criteria of physical acceptability for a stellar solution via mimic approach. Finally, we show that the compactness factor in the presence of gravitational decoupling satisfies the Buchdahal limit under 5D EGB gravity.

Role of Complexity on Self‐gravitating Compact Star by Gravitational Decoupling

AbstractIn this paper, we study novel classes of solutions characterizing the role of complexity on static and spherically symmetric self‐gravitating systems proposed by L. Herrera (Phys Rev D 97: 044010, 2018) in the gravitational decoupling background. We start by considering the minimal geometric deformation approach as a ground‐breaking tool for generating new physically viable models for anisotropic matter distributions by exploiting the Buchdahl and Tolman models. In both models, all solutions show similar results with a slight change in their magnitude for a non‐vanishing complexity factor i.e., , where β is a decoupling constant. However, under vanishing complexity factor i.e., , the minimally deformed anisotropic Buchdahl model yielded a constant density isotropic fluid distribution and anisotropic matter distribution becomes an isotropic fluid matter distribution without invoking any isotropy requirement. On the other hand, Tolman model possesses an increasing pressure when the complexity factor vanishes. Furthermore, we also extend our findings by calculating the mass‐complexity factor relationship for both presented models, revealing that the mass is larger for small values of the decoupling constant β and the complexity factor .

Self-gravitating anisotropic star using gravitational decoupling

This paper addresses a new gravitationally decoupled anisotropic solution for the compact star model via the minimal geometric deformation (MGD) approach. We consider a non-singular well-behaved gravitational potential corresponding to the radial component of the seed spacetime and embedding Class I condition that determines the temporal metric function to solve the seed system completely. However, two different well-known mimic approaches such as and have been employed to determine the deformation function which gives the solution of the second system corresponding to the extra source. In order to test the physical viability of the solution, we have checked several conditions such as regularity conditions, energy conditions, causality conditions, hydrostatic equilibrium, etc. Moreover, the stability of the solutions has been also discussed by the adiabatic index and its critical value. We find that the solutions set seems viable as far as observational data are concerned.

Anisotropic counterpart of charged Durgapal V perfect fluid sphere

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

Gravitational decoupled anisotropic spherical solutions in f(R, T) gravity by minimal geometric deformation approach

This article deals with the new systematic approach that is gravitational decoupling via minimal geometric deformation (MGD) approach. Here, we present the anisotropic spherical solution in f(R, T) gravity by adopting MGD approach. For this, we consider the Tolman V isotropic solution and extend it to anisotropic domain. For comprehensive results in f(R, T) theory, we assume viable model which is a linear combination of generalized Starobinsky f(R) model (Starobinsky 1980 Phys. Lett. B 91, 99) and λT (where T is the trace of T ij ). We are producing two different versions of anisotropic solution adopting two different mimic constraints. This technique helps us to find the new groups of anisotropic solutions through a single isotropic solution. We analyze the physical behavior of the anisotropic solutions through energy conditions and causality conditions. The graphical representation shows that both solutions satisfy all the energy conditions for different ranges of parameters. We conclude that both obtained models present the realistic behavior satisfying the all physical constraints and stability criterion.

Minimally deformed anisotropic stars by gravitational decoupling in Einstein\u2013Gauss\u2013Bonnet gravity

In this article, we develop a theoretical framework to study compact stars in Einstein gravity with the Gauss–Bonnet (GB) combination of quadratic curvature terms. We mainly analyzed the dependence of the physical properties of these compact stars on the Gauss–Bonnet coupling strength. This work is motivated by the relations that appear in the framework of the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling), we establish an exact anisotropic version of the interior solution in Einstein–Gauss–Bonnet gravity. In fact, we specify a particular form for gravitational potentials in the MGD approach that helps us to determine the decoupling sector completely and ensure regularity in interior space-time. The interior solutions have been (smoothly) joined with the Boulware–Deser exterior solution for 5D space-time. In particular, two different solutions have been reported which comply with the physically acceptable criteria: one is the mimic constraint for the pressure and the other approach is the mimic constraint for density. We present our solution both analytically and graphically in detail.

Gravitational Decoupling in Higher Order Theories

Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically symmetric solutions of the Einstein-scalar system from the Schwarzschild vacuum metric. This was then used to investigate the effect of scalar fields on the Schwarzschild black hole solution. We show that this method can be extended to higher order theories. In particular, we consider fourth order Einstein–Weyl gravity, and in this case by using the Schwarzschild metric as a seed solution to the associated vacuum field equations, we apply the MGD method to generate a solution to the Einstein–Weyl scalar theory representing a hairy black hole solution. This solution is expressed in terms of a series using the Homotopy Analysis Method (HAM).

Ultracompact stars with polynomial complexity by gravitational decoupling

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.

Gravitationally decoupled non-static anisotropic spherical solutions

This paper is devoted for the formulation of new anisotropic solutions for non-static spherically symmetric self-gravitating systems through gravitational decoupling technique. Initially, we add a gravitational source in the perfect matter distribution for inducing the effects of anisotropy in the considered model. We then decouple the field equations through minimal geometric deformation approach and derive three new anisotropic solutions. Among these, two anisotropic solutions are evaluated by applying specific constraints on anisotropic source and the third solution is obtained by employing the barotropic equation of state. The physical acceptability and stability of the anisotropic models are investigated through energy conditions and causality condition, respectively. We conclude that all the derived anisotropic solutions are physically viable as well as stable.

Anisotropic charged compact stellar configurations in the perspective of gravitational decoupling approach

We construct the physically admissible charged compact star models threaded with anisotropic matter contents via gravitational decoupling approach. Durgapal IV solution containing charge is considered as seed solution for applying minimal geometric deformation approach. We extend the isotropic seed solution into anisotropic domain by imposing suitable mimic constraints on the physical variables i.e. pressure and density. The extended solution is employed to frame the models of dense relativistic structures. We study the geometrical and thermodynamic behavior of the models and examine the physically admissible attributes of the models via graphical patterns. The stability status of the compact entities is examined through different stability criteria. The essential energy bounds are found to be satisfied within the compact star models. We performed the extensive analysis of the model for the star RXJ 1856-37 having mass 0.9 M Θ and radius 6 km. The extended anisotropic solution is also compatible with observed masses as well as radii of some compact stars EXO 1785-248 and PSR J1614-2230.

Minimally deformed charged anisotropic spherical solution

The present article is dedicated to the study of charged anisotropic solutions in the background of gravitational decoupling via. minimal geometric deformation (MGD) approach. In this work, we emphasize on the background of MGD that how this MGD approach works. Here, we have minimally deformed the radial component of the spacetime as $$e^{-\lambda }\longrightarrow \mu +\alpha \,f(r)$$ , where $$\alpha $$ is a coupling constant. Next, we determined the decoupler function f(r) by using well-known constraints procedure, namely mimic constraints to the radial pressure, and then components for the $$\theta $$ –sector governed by extra source. The obtained decoupler function f(r) vanishes at the center as well as on the stellar boundary. The constants involved in the solution have been determined by using well-known Reissner–Nordstrom solution. Finally, we have presented the graphical representation with detailed analysis for describing the physical and astrophysical viability of the solution through the modeling of the stellar objects.

An anisotropic version of Tolman VII solution in f(R, T) gravity via gravitational decoupling MGD approach

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 $\phi_{ij}$. Following MGD approach, the set of field equations has been separated into two sections. One section represents $f(R, T)$ field equations, while the other is related to the source $\phi_{ij}$. The matching conditions for inner and outer geometry have also been discussed and an anisotropic solution has been developed using mimic constraint for radial pressure. In order to check viability of the solution, we have considered observation data of three different compact star models, named PSR J1614-2230, PSR 1937+21 and SAX J1808.4-3658 and have discussed thermodynamical properties analytically and graphically. The energy conditions are found to be satisfied for the three compact stars. The stability analysis has been presented through causality condition and Herrera's cracking concept, which ensures physical acceptability of the solution.

Durgapal IV model considering the minimal geometric deformation approach

The present article reports the study of local anisotropic effects on Durgapal's fourth model in the context of gravitational decoupling via the minimal geometric deformation approach. To achieve this, the most general equation of state relating the components of the θ−sector is imposed to obtain the decoupler function . In addition, certain properties of the obtained solution, such as the behavior of the salient material content threading the stellar interior; causality and energy conditions; hydrostatic balance through the modified Tolman−Oppenheimer−Volkoff conservation equation and stability mechanism against local anisotropies using the adiabatic index; sound velocity of the pressure waves; convection factor; and the Harrison−Zeldovich−Novikov procedure, are investigated to check whether 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 the adiabatic index and Harrison−Zeldovich−Novikov case. To produce a more realistic picture, the numerical data for some known compact objects were determined and different values of the parameter were considered to compare with the GR case, i.e., .