Compact elastic objects in general relativity

TL;DR

This paper develops a comprehensive framework for studying self-gravitating elastic materials in general relativity, demonstrating how elasticity can increase maximum mass and compactness of stellar models, and exploring their stability and physical viability.

Contribution

It introduces a rigorous general relativistic framework for elastic stars and analyzes their stability, mass-radius relations, and physical properties, expanding understanding of ultracompact objects.

Findings

Elasticity increases maximum stellar mass by up to 22%.

Some elastic stars can reach high compactness while remaining stable.

Radial instability occurs beyond maximum mass, similar to perfect-fluid stars.

Abstract

We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic stars. We present the mass-radius ($M-R$) diagram for various families of models, showing that elasticity contributes to increase the maximum mass and the compactness up to $\approx 22\%$, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as $GM/(c^2R)\approx 0.35$ while remaining stable under radial perturbations and satisfying all energy conditions and subluminal wave propagation, thus being physically realizable models of stars with a light ring. We provide numerical evidence that radial instability occurs for central densities larger than that corresponding to the maximum mass, as in the perfect-fluid case. Elasticity may be a key ingredient to build consistent models of exotic ultracompact objects and black-hole mimickers, and can also be relevant for a more accurate modelling of the interior of neutron stars.