An Exact Model of an Anisotropic Relativistic Sphere

Abstract

In this paper the field equations of general relativity are solved to obtain an exact solution for a static anisotropic fluid sphere. The solution is free from singularity and satisfies the necessary physical requirements. The physical 3-space of the solution is pseudo-spheroidal. The solution is matched at the boundary with the Schwarzschild exterior solution. Numerical estimates of various physical parameters are briefly discussed.

The role of pressure anisotropy on the maximum mass of cold compact stars

“…Different solutions of Einstein's field equations for anisotropic fluid distribution with spheroidal geometry, with varying forms of the energy density, have been obtained by many workers [13][14][15][16]. So far, the role of pressure anisotropy has been extensively studied in the context of high red-shift values and stability of compact objects (see for example [17][18][19] and references therein).…”

Maximum bounds on the surface redshift of anisotropic stars

“…[5]. The application of anisotropic fluid models to neutron stars began with the pioneering work of Bowers and Liang [6] and was done both analytically and numerically [7][8][9][10][11][12][13][14][15]. Some recent work may be found in Refs.…”

Analytical study of anisotropic compact star models

“…Solutions, containing free Δ, exist in several combinations. Thus Δ, ρ solutions either simplify the TOV equation [75,76] or the Einstein equations, which acquire simple solutions [77,78], or even such in hypergeometric functions [79,80].…”