Spherically symmetric elastic bodies in general relativity

TL;DR

This paper reviews the study of spherically symmetric elastic bodies in general relativity, introducing new definitions, analyzing stability, and numerically exploring mass-radius relationships to understand their physical limits.

Contribution

It presents a new framework for defining and analyzing spherically symmetric elastic bodies in general relativity, including stability and maximum compactness conjectures.

Findings

Established invariant criteria for initial data

Numerically constructed mass-radius diagrams

Conjectured maximum stable compactness

Abstract

The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502 (2022)], and [arXiv:2306.16584 [gr-qc]], where we introduced a new definition of spherically symmetric elastic bodies in general relativity, and applied it to investigate the existence and physical viability, including radial stability, of static self-gravitating elastic balls. We focus on elastic materials that generalize fluids with polytropic, linear, and affine equations of state, and discuss the symmetries of the energy density function, including homogeneity and the resulting scale invariance of the TOV equations. By introducing invariant characterizations of physical admissible initial data, we numerically construct mass-radius-compactness diagrams, and conjecture about the maximum compactness of stable physically admissible elastic balls.