The static spherically symmetric body in relativistic elasticity

TL;DR

This paper explores static spherically symmetric solutions in relativistic elasticity, comparing two matter models based on their stored energy functionals, and examines their behavior under large deformations.

Contribution

It introduces and compares two relativistic matter models with different strain variables, analyzing their properties in static spherically symmetric settings.

Findings

Both models approximate classical elastic materials for small strains.

Differences emerge in the behavior under large deformations.

The study provides insights into relativistic elastic matter in gravitational fields.

Abstract

In this paper is discussed a class of static spherically symmetric solutions of the general relativistic elasticity equations. The main point of discussion is the comparison of two matter models given in terms of their stored energy functionals, i.e., the rule which gives the amount of energy stored in the system when it is deformed. Both functionals mimic (and for small deformations approximate) the classical Kirchhoff-St.Venant materials but differ in the strain variable used. We discuss the behavior of the systems for large deformations.