Static self-gravitating elastic bodies in Einstein gravity

TL;DR

This paper proves the existence of unique static solutions to Einstein's equations coupled with relativistic elasticity for small gravitational constants, even without symmetry assumptions, by constructing small deformations of relaxed configurations.

Contribution

It provides the first proof of static Einstein-elastic solutions without symmetry, expanding understanding of relativistic elastic bodies in gravity.

Findings

Existence of static solutions for small gravitational constants

Solutions are small deformations of relaxed configurations

First proof of non-symmetric static Einstein-elastic solutions

Abstract

We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations without symmetries.