Static conformal elastic solution of Einstein's field equations

TL;DR

This paper derives new static elastic solutions to Einstein's field equations using conformal transformations of known solutions, analyzing their physical viability and matching conditions.

Contribution

It introduces a novel method for constructing static elastic solutions via conformal transformations of Reissner-Nordström-de Sitter spacetime.

Findings

Conformal factors for elastic matter are explicitly obtained.

Energy conditions are analyzed for the new solutions.

Matching conditions with exterior spacetime are discussed.

Abstract

In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the Reissner-Nordstr\"{o}m-de Sitter solution. The conformal factors for static space-time structure with an elastic matter are obtained. Further, we analyze the viability of energy conditions. And also discuss the matching problem with the exterior space-time.