Self-gravitating elastic bodies

TL;DR

This paper discusses models of finite self-gravitating elastic bodies in general relativity, providing a rigorous framework for the initial value problem of extended objects, moving beyond idealized point-like sources.

Contribution

It introduces a rigorous approach to modeling finite self-gravitating elastic bodies in GR, advancing the understanding of their initial value problem.

Findings

Provides a mathematical framework for finite extended objects in GR

Establishes initial value problem for self-gravitating elastic bodies

Moves beyond point-like source models

Abstract

Extended objects in GR are often modelled using distributional solutions of the Einstein equations with point-like sources, or as the limit of infinitesimally small "test" objects. In this note, I will consider models of finite self-gravitating extended objects, which make it possible to give a rigorous treatment of the initial value problem for (finite) extended objects.