Exact Solutions: Anisotropic Stars in Terms of Pressure

TL;DR

This paper derives exact solutions for anisotropic star models using a generalized TOV equation, expressing radial pressure as an invertible function of a variable w, and explores various anisotropy forms and negative density gradient solutions.

Contribution

It introduces a method to obtain exact anisotropic star solutions with pressure as a function of w, expanding previous models and including solutions with negative density gradients.

Findings

Derived general solutions for anisotropic stars in terms of w.

Presented new solutions with different anisotropy factors.

Explored solutions with negative density gradient.

Abstract

Dev (2002) discussed some exact solutions of anisotropic stars for special forms of TOV for constant energy density. Considering Bijalwan (2011) ansatz for charged perfect fluids we present here some exact solutions to the generalized TOV equation for anisotropic fluids by representing equation in terms for radial pressure. Consequently, radial pressure is found to be an invertible arbitrary function of w(=c1+c2r^2), where c1 and c2 is nonzero are arbitrary constants, and r is the radius of star, i.e. p=p(w) . We present a general solution for anisotropic fluid in terms for w. We list and discuss some old and new solutions which fall in this category. Consequently, we present solutions for generalized TOV considering different forms of anisotropy factor in terms of w. Also, we investigated solutions of generalized TOV with negative density gradient (NDG).