Rotating elastic bodies in Einstein gravity

TL;DR

This paper proves the existence and uniqueness of stationary, axisymmetric solutions in Einstein gravity for small gravitational constants and angular frequencies, describing rotating elastic bodies in a relativistic setting.

Contribution

It establishes a rigorous mathematical result connecting relativistic elasticity with Einstein gravity for rotating bodies, extending previous non-relativistic models.

Findings

Existence of solutions for small gravitational constants and frequencies

Uniqueness of these solutions under given conditions

Solutions describe rigidly rotating elastic bodies in Einstein gravity

Abstract

We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations coupled to the equations of relativistic elasticity with the body performing rigid rotations around the symmetry axis at the given angular frequency.