Static conformal models for anisotropic charged fluids

Abstract

We investigate the role played by conformal symmetries in the study of exact solutions in static spherically symmetric spacetimes. We consider the gravitational field associated with anisotropic charged fluids. The existence of a conformal symmetry provides us with a functional relation between the metric functions. This relationship yields a general solution to the Einstein-Maxwell equations. Various conformally symmetric models for fluids that are charged or anisotropic or both are shown to be special cases of the general exact solution generated in this paper. In particular we generate a conformally flat Finch-Skea type model for an isotropic charged fluid.

Generating solutions for charged stellar models in general relativity

“…These expressions were put into Eq. (36) and another equation for y arises, which is simpler [63]. Solutions based on ψ in Eq.…”

A Tolman-like Compact Model with Conformal Geometry

“…where C a bcd are the nonzero components of the Weyl tensor. Recently, it was showed by Manjonjo et al [29] that the existence of a conformal symmetry (9) in the spacetime manifold, together with the integrability condition (11), lead to a relationship between the gravitational potentials y and Z known as the conformal condition…”

“…Detailed studies involving conformal motions in static spherically symmetric spacetimes have been performed recently by Tupper et al [25] and Maartens et al [26,27]. Manjonjo et al [28,29] used the Weyl tensor for conformally flat and non-conformally flat spacetimes to establish a relationship between the static metric potentials. An extensive investigation of exact models for compact objects has been performed by Mafa Takisa et al [30] and Kileba Matondo et al [31,32] with the help of this conformal relationship.…”

“…In addition, the conformal Killing vector produces models which are physically realistic [30][31][32][33][34][35][36][37][38]. The existence of a conformal Killing vector in spherically symmetric spacetimes gives a relationship between the gravitational potentials [28,29].This provides a systematic approach of generating new exact solutions to the Einstein-Maxwell field equations. Stellar models generated in this approach, characterized by a spacetime symmetry, are physically acceptable and produce values for masses and radii corresponding to observed relativistic stars.…”

“…In this investigation, we aim to generate a new class of charged anisotropic solutions for compact stars invariant under conformal symmetry via the generalized condition of anisotropic pressure established in Manjonjo et al [29]. Most of the solutions for compact stars found with conformal symmetry are not regular at the center.…”