(N+2)-Dimensional Anisotropic Charged Fluid Spheres with Pressure: Riccati Equation

TL;DR

This paper derives exact solutions for (N+2)-dimensional static anisotropic charged fluid spheres in general relativity, expressing key physical quantities in terms of pressure and reducing the problem to solving a Riccati equation.

Contribution

It extends previous methodologies to higher dimensions and provides a general solution framework for anisotropic charged fluids using Riccati equations.

Findings

Solutions express metrics, density, and electric field in terms of pressure.

Radial pressure is an invertible function of a quadratic radius term.

Solutions satisfy a barotropic equation of state.

Abstract

General exact (N+2)-dimensional,n>=2 solutions in general theory of relativity of Einstein-Maxwell field equations for static anisotropic spherically symmetric distribution of charged fluid are expressed in terms of radial pressure. Subsequently, metrics (e(lambda) and e(nu)), matter density and electric intensity are expressible in terms of pressure. We extend the methodology used by Bijalwan (2011a, 2011c, 2011d) for charged and anisotropic fluid. Consequently, radial pressure is found to be an invertible arbitrary function of w(c1+c2r^2), where c1 and c2(non zero) are arbitrary constants, and r is the radius of star, i.e. p=p(w) . We present a general solution for static anisotropic charged pressure fluid in terms for w. We reduce to the problem of finding solutions to anisotropic charged fluid to that of finding solutions to a Riccati equation. Also, these solutions satisfy barotropic equation of state relating the radial pressure to the energy density.