Influence of Electromagnetic Field on Hyperbolically Symmetric Source

TL;DR

This paper investigates how electromagnetic fields influence hyperbolically symmetric static sources in spacetime, revealing negative energy densities and the necessity of quantum effects for physical plausibility.

Contribution

It extends previous work by analyzing electromagnetic effects on hyperbolically symmetric sources, providing explicit solutions and exploring their physical implications.

Findings

Negative energy density in the source

Presence of a vacuole near the center

Explicit exact solutions derived

Abstract

We pursue a coherent analysis of hyperbolically symmetric static sources by extending the work of Herrera \cite{26} to the case of electromagnetic field. We deeply analyze the impact of such a force on the physical characteristics of the hyperbolically symmetric spacetime under consideration. Setting off the Einstein's gravitational equations, we particularize the stress-energy tensor by keeping in mind the constituents of tetrad field in Minkowski coordinate system. Hyperbolically symmetric source has a vacuole in the vicinity of its center, i.e., such a distribution is unable to fill the central zone of symmetry. In all the stellar expressions, the energy density of the source comes out to be negative which demonstrates that quantum effects must be involved along with certain extreme restrictions to explicate any physical application of such a hyperbolically symmetric source. Various explicit exact solutions along with their corresponding generating functions are also worked out.