Studies an analytic model of a spherically symmetric compact object in Einsteinian gravity

Abstract We propose a new compact stellar object model existing in a space filled with a distribution of anisotropic fluid matter for stellar configuration exposed to the hydrostatic equilibrium. An analytical solution was obtained using dark-energy (DE), which is characterized by a equation of state (EoS) of the type $$p=\gamma \rho - \rho$$ p=γρ-ρ corresponding to the external Schwarzschild vacuum solution through a thin envelope. We have imposed a collective function based on an adjustable coefficient to solve the Einstein field equations (EFEs). We investigate the general physical characteristics of high-density astrophysical objects based on the required solutions, with the inside structure of the stellar objects, such as the energy conditions, stability analysis, mass function, surface redshift function, velocity of sound and compactness of stellar objects through theoretical expression as well as graphic plots. In terms of our results, the physical behavior of this model can be used to model ultra-compact objects

A spherically symmetric model of anisotropic fluid for strange quark spheres

Abstract In the present work, we try to find a solution without singularity of Einstein's field equations for the spherically symmetric perfect fluid objects, accurately strange quark spheres, taking into consideration Schwarzschild metric as the outside space-time. An ensemble of inside solutions found on the basis of the simplest linear state equation in the specific form $$p_r =\alpha \rho -\beta$$ pr=αρ-β . The energy density $$\rho (r)$$ ρ(r) , the radial pressure $$p_r (r)$$ pr(r) and the tangential pressure $$p_t (r)$$ pt(r) are devoid of any singularity and exhibit a well-behaved nature within the generalized anisotropic solution for compact spherical object. The generalized TOV equation is very much preserved inside the system and all energy conditions are excellent. The stability of the matter distribution of our system is checked by the concept of Herrera's cracking and the condition of causality is all around fulfilled for our models. The adiabatic index of our specific configuration is greater than 4 / 3 in all interior points of the system and the mass-to-radius ratio in our situation is determined also lies within the Buchdahl limit i.e. $$\hbox {M}/\hbox {R}\le 4/3\,\left( {\approx 0.444} \right)$$ M/R≤4/3≈0.444 . We explore the physical characteristics based on the analytical model developed for relativistic compact stellar spheres inside the framework of the general theory of relativity. The evaluated mass and radius are in close concurrence with the observational information. We show that various physical characteristics of the known strange spherical object, viz. PSR J1614-2230, Vela X-1, 4U 1608-52, PSR J1903+327, 4U 1820-30, Cen X-3, Her X-1, and SAX J1808.4-3658, can be described by the current model

Anisotropic compact stars via embedding approach in general relativity: new physical insights of stellar configurations

AbstractThe main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential $$\lambda (r)$$ λ ( r ) , and we obtained the other metric potential $$\nu (r)$$ ν ( r ) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars

Anisotropic Karmarkar stars in f(R, T)-gravity

The main aim of this work is devoted to studying the existence of compact spherical systems representing anisotropic matter distributions within the scenario of alternative theories of gravitation, specifically f(R, T) gravity theory. Besides, a noteworthy and achievable choice on the formulation of f(R, T) gravity is made. To provide the complete set of field equations for the anisotropic matter distribution, it is considered that the functional form of f(R, T) as $$f(R, T)=R+2\chi T$$ f(R,T)=R+2χT , where R and T correspond to scalar curvature and trace of the stress–energy tensor, respectively. Following the embedding class one approach employing the Eisland condition to get a full space–time portrayal interior the astrophysical structure. When the space–time geometry is identified, we construct a suitable anisotropic model by using a new gravitational potential $$g_{rr}$$ grr which often yields physically motivated solutions that describe the anisotropic matter distribution interior the astrophysical system. The physical availability of the obtained model, represents the physical characteristics of the solution is affirmed by performing several physical tests. It merits referencing that with the help of the observed mass values for six compact stars, we have predicted the exact radii for different values of $$\chi$$ χ -coupling parameter. From this one can convince that the solution predicted the radii in good agreement with the observed values. Since the radius of MSP J0740+6620, the most massive neutron star observed yet is still unknown, we have predicted its radii for different values of $$\chi$$ χ -coupling parameter. These predicted radii exhibit a monotonic diminishing nature as the parameter $$\chi$$ χ going from $$-1$$ -1 to 1 gradually. The M–R curve generated from our solution can accommodate a variety of compact stars from the less massive (Her X-1) to super massive (MSP J0740+6620). So the present study uncovers that the modified f(R, T) gravity is an appropriate theory to clarify massive astrophysical systems, in any case, for $$\chi =0.0$$ χ=0.0 the standard consequences of the general relativity are recovered

Anisotropic relativistic fluid spheres: an embedding class I approach

Abstract In this work, we present a new class of 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 perform our analysis by proposing a new metric potential $$g_{rr}$$ grr which yields us a physically viable performance of all physical variables. The obtained model is representing the physical features of the solution in detail, analytically as well as graphically for strange star candidate SAX J1808.4-3658 ($$Mass=0.9 ~M_{\odot }$$ Mass=0.9M⊙ , $$radius=7.951$$ radius=7.951 km), with different values of parameter n ranging from 0.5 to 3.4. Our suggested solution is free from physical and geometric singularities, satisfies causality condition, Abreu's criterion and relativistic adiabatic index $$\varGamma$$ Γ , and exhibits well-behaved nature, as well as, all energy conditions and equilibrium condition are well-defined, which implies that our model is physically acceptable. The physical sensitivity of the moment of inertia (I) obtained from the solutions is confirmed by the Bejger−Haensel concept, which could provide a precise tool to the matching rigidity of the state equation due to different values of n viz., $$n=0.5, 1.08, 1.66, 2.24, 2.82$$ n=0.5,1.08,1.66,2.24,2.82 and 3.4

Influence of three parameters on maximum mass and stability of strange star under linear f(Q)−f(Q)-action

This study simulates strange stars in $f(Q)$ gravity with an additional source under an electric field using gravitational decoupling and the complete Gravitational Decoupling (CGD) technique. By employing the Tolman ansatz and the MIT bag model equation of state (EOS), we explore bounded star configurations derived from the $\theta_0^0 = \rho$ and $\theta_1^1 = p_r$ sectors within the CGD formalism. Our models are subjected to physical viability tests, and we analyze the impact of anisotropy and the electric charge parameter $E_0$ as well as the coupling parameters $\alpha$ and $\beta_1$. Comparisons are made with observational constraints, including GW190814, neutron stars PSR J1614-2230, PSR J1903+6620, Cen X-3 and LMC X-4. Notably, we achieve the presence of a lower "\textit{mass gap}" component by adjusting parameters $\alpha$ and $\beta_1$. Our models exhibit well-behaved mass profiles, internal regularity, and stability, with the absence of gravitational collapse verified through the Buchdahl--Andr\'{e}asson's limit. In addition, we present a detailed physical analysis based on three parameters, $\alpha$ (decoupling strength), $\beta_1$ ($f(Q)$--coupling) and $Q$ (surface charge). This study provides insights into the behavior of compact objects in $f(Q)$ gravity and expands our understanding of strange star configurations within this framework.Comment: 18 pages, 18 figures, Accepted version Monthly Notices of Royal Astronomical Societ

Gravitationally decoupled charged anisotropic solutions in Rastall gravity

This paper develops the stellar interior geometry for charged anisotropic spherical matter distribution by developing an exact solution of the field equations of Rastall gravity using the notion of gravitational decoupling. The main purpose of this investigation is the extension of the well-known isotropic model within the context of charged isotropic Rastall gravity solutions. The second aim of this work is to apply gravitational decoupling via a minimal geometric deformation scheme in Rastall gravity. Finally, the third one is to derive an anisotropic version of the charged isotropic model previously obtained by applying gravitational decoupling technology. We construct the field equations which are divided into two sets by employing the geometric deformation in radial metric function. The first set corresponds to the seed (charged isotropic) source, while the other one relates the deformation function with an extra source. We choose a known isotropic solution for spherical matter configuration including electromagnetic effects and extend it to an anisotropic model by finding the solution of the field equations associated with a new source. We construct two anisotropic models by adopting some physical constraints on the additional source. To evaluate the unknown constants, we use the matching of interior and exterior spacetimes. We investigate the physical feasibility of the constructed charged anisotropic solutions by the graphical analysis of the metric functions, density, pressure, anisotropy parameter, energy conditions, stability criterion, mass function, compactness, and redshift parameters. For the considered choice of parameters, it is concluded that the developed solutions are physically acceptable as all the physical aspects are well-behaved