Higher Dimensional Extension of Charged and Neutral Fluid Spheres with Pressure

Abstract

General exact higher-dimensional (n+2), n>2 solutions in general theory of relativity of Einstein-Maxwell field equations for spherically symmetric distribution of charged pressure perfect fluid are expressed in terms of pressure extending 4-dimensional solutions presented by Bijalwan (Astrophys. Space Sci. 2011, doi:10.1007/s10509-011-0691-0). Subsequently, metrics (eλ and eυ), matter density and electric intensity are expressible in terms of pressure. Consequently, Pressure is found to be an invertible arbitrary function of ω (=c1+c2r2), where c1 and c2 (≠0) are arbitrary constants, and r is the radius of star, i.e. p=p(ω). We present a general solution for charged pressure fluid in terms for ω. We list and discuss some old and new solutions which fall in this category. Also, these solutions satisfy barotropic equation of state relating the radial pressure to the energy density. But we noticed that none of these solutions in terms of pressure for charged fluids has a well behaved neutral counter part for a spatial component of metric eλ i.e. choosing same spatial component for charged and neutral fluid. To illustrate the approach, we discovered a new solution for extended charged analogues of Schwarzschild interior solution in higher dimensions which is found to be well behaved only for n=2. The maximum mass found to be 1.512 MΘ with linear dimension 14.964 km. Physical quantities pressure, energy density, red-shift, velocity of sound and p/c2ρ are well behaved and monotonically decreasing towards the surface while adiabatic index and charge density are monotonically increasing. For brevity we don’t discuss the numerical results in detailed.