AN EXACT SOLUTION OF EINSTEIN EQUATIONS FOR INTERIOR FIELD OF AN ANISOTROPIC FLUID SPHERE

Lakshmi S. Desai

Abstract: In this paper, an anisotropic relativistic fluid sphere with variable density, which decreases along the radius and is maximum at the centre, is discussed. Spherically symmetric static space-time with spheroidal physical 3-space is considered. The source is an anisotropic fluid. The solution is an anisotropic generalization of the solution discussed by Vaidya and Tikekar [1]. The physical three space constant time has spheroidal solution. The line element of the solution can be expressed in the form Patel and Desai [2]. The material density is always positive. The solution efficiently matches with Schwarzschild exterior solution across the boundary. It is shown that the model is physically reasonable by studying the numerical estimates of various parameters. The density vs radial pressure relation in the interior is discussed numerically. An anisotropy effect on the redshift is also studied numerically

Keywords: Cosmology, Anisotropic fluid sphere, Radial pressure, Radial density, Relativistic model

DOI: https://doi.org/10.15623/ijret.2015.0412055