A Tolman-like Compact Model with Conformal Geometry.

Sunil D. Maharaj,Didier Kileba Matondo

doi:10.3390/e23111406

Abstract

In this investigation, we study a model of a charged anisotropic compact star by assuming a relationship between the metric functions arising from a conformal symmetry. This mechanism leads to a first-order differential equation containing pressure anisotropy and the electric field. Particular forms of the electric field intensity, combined with the Tolman VII metric, are used to solve the Einstein–Maxwell field equations. New classes of exact solutions generated are expressed in terms of elementary functions. For specific parameter values based on the physical requirements, it is shown that the model satisfies the causality, stability and energy conditions. Numerical values generated for masses, radii, central densities, surface redshifts and compactness factors are consistent with compact objects such as PSR J1614-2230 and SMC X-1.

Highlights

An interesting suggestion to gain a deeper understanding of self-gravitating systems is to apply the idea of complexity in theories of gravity
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]
We present all the energy conditions namely: null energy condition (NEC), weak energy condition (WEC) and strong energy condition (SEC):

Summary

Introduction

An interesting suggestion to gain a deeper understanding of self-gravitating systems is to apply the idea of complexity in theories of gravity. 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]. The Tolman VII metric function can be used to integrate the conformal Killing condition of anisotropic pressure with the help of particular forms of the electric field functions to generate new classes of exact solutions which are free from singularities.

Field Equations

Exact Solutions

Class II Solutions:

Class III Solutions:

Physical Quantities

Tolman–Oppenheimer–Volkoff Equation

Equation of State

Matching Conditions

Physical Analysis

Conclusions