Relativistic anisotropic models for compact star with equation of state p = f(ρ)

Abstract

We present new anisotropic models for Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] type perfect fluid solution. For this purpose, we started with metric potential [Formula: see text] same as Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] and [Formula: see text] is monotonically increasing function as suggested by Lake [K. Lake, Phys. Rev. D 67 (2003) 104015]. After that we determine the new pressure anisotropy factor [Formula: see text] with the help of both the metric potentials [Formula: see text] and [Formula: see text] and propose new well behaved general solution for anisotropic fluid distribution. The physical quantities like energy density, radial and tangential pressures, velocity of sound and redshift etc. are positive and finite inside the compact star. In this connection, we have studied the stability of the models, which is most vital one and also we determined the equation of state [Formula: see text] for the realistic compact star models. It is noted that the mass and radius of our models can represent the structure of realistic astrophysical objects such as Her X-1 and RXJ 1856-37.

Analytical study of anisotropic compact star models

“…The arbitrary constant in it allows one to arrange the fulfilment of Eq. (14). Since it shows that e ν(r s ) < 1, the same is true for e ν(0) and the constant in C1 is smaller than unity.…”

A conformally flat realistic anisotropic model for a compact star

“…One of the first was given in [6], where some of the Tolman isotropic solutions [7] were modified to become anisotropic. Other followed recently [8], [9], [10], [11], [12], [13], [14].…”

A new model for spherically symmetric anisotropic compact star

“…Against this background we would like to mention that in one of the earlier works Maurya et al [23] have proposed an algorithm of a charged anisotropic compact star while in the later works [24,25] they have given a new approach for finding an anisotropic solution of Einstein's field equations by using the metric potentials function. The present work is a sequel of the work done by Maurya et al [26,27], in which the authors have obtained the charged compact star and the structure of a relativistic electromagnetic mass model under the condition of a class one metric.…”