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 pr = Θ1 1 and ρ = Θ0 0 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 compact stars in higher-order curvature theory

In this paper we shall consider spherically symmetric spacetime solutions describing the interior of stellar compact objects, in the context of higher-order curvature theory of the $${{\mathrm {f(R)}}}$$ f ( R ) type. We shall derive the non-vacuum field equations of the higher-order curvature theory, without assuming any specific form of the $${{\mathrm {f(R)}}}$$ f ( R ) theory, specifying the analysis for a spherically symmetric spacetime with two unknown functions. We obtain a system of highly non-linear differential equations, which consists of four differential equations with six unknown functions. To solve such a system, we assume a specific form of metric potentials, using the Krori–Barua ansatz. We successfully solve the system of differential equations, and we derive all the components of the energy–momentum tensor. Moreover, we derive the non-trivial general form of $${{\mathrm {f(R)}}}$$ f ( R ) that may generate such solutions and calculate the dynamic Ricci scalar of the anisotropic star. Accordingly, we calculate the asymptotic form of the function $${\mathrm {f(R)}}$$ f ( R ) , which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in [1], with the latter also resulting to a non-trivial form of the Ricci scalar. Notably but rather expected, the exterior solution differs from the Schwarzschild one in the context of general relativity. The matching procedure will eventually relate two constants with the mass and radius of the compact stellar object. We list the necessary conditions that any compact anisotropic star must satisfy and explain in detail that our model bypasses all of these conditions for a special compact star $$\textit{Her X--1}$$ Her X - - 1 , which has an estimated mass and radius $$(mass = 0.85 \pm 0.15M_{\circledcirc }\ and\ radius = 8.1 \pm 0.41~\text {km}$$ ( m a s s = 0.85 ± 0.15 M ⊚ a n d r a d i u s = 8.1 ± 0.41 km ). Moreover, we study the stability of this model by using the Tolman–Oppenheimer–Volkoff equation and adiabatic index, and we show that the considered model is different and more stable compared to the corresponding models in the context of general relativity.

Equilibrium, radial stability and non-adiabatic gravitational collapse of anisotropic neutron stars

In this work we construct families of anisotropic neutron stars for an equation of state compatible with the constraints of the gravitational-wave event GW170817 and for four anisotropy ansatze. Such stars are subjected to a radial perturbation in order to study their stability against radial oscillations and we develop a dynamical model to describe the non-adiabatic gravitational collapse of the unstable anisotropic configurations whose ultimate fate is the formation of a black hole. We find that the standard criterion for radial stability $$dM/d\rho _c >0$$dM/dρc>0 is not always compatible with the calculation of the oscillation frequencies for some anisotropy ansatze, and each anisotropy parameter is constrained taking into account the recent restriction of maximum mass of neutron stars. We further generalize the TOV equations within a non-adiabatic context and we investigate the dynamical behaviour of the equation of state, heat flux, anisotropy factor and mass function as an unstable anisotropic star collapses. After obtaining the evolution equations we recover, as a static limit, the background equations.

Modelling of a compact anisotropic star as an anisotropic fluid sphere in f(T) gravity

In this article, the authors have discussed a new exact model of anisotropic stars in the f(T) theory of gravity. A parametric form of the metric functions has been implemented to solve the dynamical equations in f(T) theory with the anisotropic fluid. The novelty of the work is that the obtained solutions do not contain singularity but are potentially stable. The estimated values for mass and radius of the different strange stars, RX J 1856–37, Her X-1, and Vela X-12, have been utilized to find the values of unknown constants in Krori and Barua metrics. The physical parameters like anisotropy, stability, and redshift of the stars have been examined in detail.

Anisotropic charged compact star of embedding class I

In this paper, we present a model of a compact relativistic anisotropic star in the presence of an electric field. In order to obtain an exact solution of the Einstein–Maxwell field equations, we assume that the stellar material inside the star obeys a Chaplygin equation of state which is a nonlinear relationship between the radial pressure and the matter density. Using Tolman’s metric potential for [Formula: see text], we obtain the other metric co-efficient by employing the Karmarkar condition which is a necessary and sufficient condition for the interior spacetime of our model to be of embedding class I. Our stellar model is free from central singularity and obeys all the conditions for a realistic stellar object.

A new solution of embedding class I representing anisotropic fluid sphere in general relativity

In this paper, we are willing to develop a model of an anisotropic star by choosing a new [Formula: see text] metric potential. All the physical parameters like the matter density, radial and transverse pressure are regular inside the anisotropic star, with the speed of sound less than the speed of light. So the new solution obtained by us gives satisfactory description of realistic astrophysical compact stars. The model of this paper is compatible with observational data of compact objects like RX J1856-37, Her X-1, Vela X-12 and Cen X-3. A particular model of Her X-1 (Mass 0.98 [Formula: see text] and radius[Formula: see text]=[Formula: see text]6.7 km.) is studied in detail and found that it satisfies all the condition needed for physically acceptable model. Our model is described analytically as well as with the help of graphical representation.