Generalized relativistic anisotropic models for compact stars

TL;DR

This paper develops new anisotropic models for compact stars by generalizing Buchdahl's solution, constructing a pressure anisotropy factor, and analyzing physical properties to match realistic astrophysical objects.

Contribution

It introduces a novel anisotropic solution for compact stars using a specific metric potential and pressure anisotropy, extending previous models.

Findings

Physical quantities are positive and finite inside the star.

Models can represent realistic objects like Her X-1 and RXJ1856-37.

Mass and radius are consistent with observed compact stars.

Abstract

We present new anisotropic generalization of Buchdahl [1] type perfect fluid solution by using the method of earlier work [2]. In similar approach we have constructed the new pressure anisotropy factor ${\Delta}$ by the help both the metric potential $e^{\lambda}$ and $e^{\nu}$. The metric potential $e^{\lambda}$ same as Buchdahl [1] and $e^{\nu}$ is monotonic increasing function as suggested by Lake [3]. After that we obtain new well behaved general solution for anisotropic fluid distribution. We calculated the physical quantities like energy density, radial and tangential pressures, velocity of sound and red-shift etc. We observe that these quantities are positive and finite inside the compact star. Also note that mass and radius of our models can represent the structure of realistic astrophysical objects such as like Her X-1 and RXJ1856-37.