Evolution equations for a wide range of Einstein-matter systems

TL;DR

This paper develops a general first-order hyperbolic framework for Einstein-matter systems using an orthonormal frame approach, applicable to various matter models including dust, perfect fluids, and elastic matter.

Contribution

It introduces a unified method for hyperbolic reduction of Einstein equations with diverse matter fields, expanding analytical tools for gravitational systems.

Findings

Framework covers dust and perfect fluid cases

Demonstrates constraint propagation in Einstein-matter systems

Provides a basis for analyzing self-gravitating elastic matter

Abstract

We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and perfect fluid. We also provide a discussion of self-gravitating elastic matter. The frame is Fermi-Walker propagated and coordinates are chosen such as to satisfy the Lagrange condition. We show the propagation of the constraints of the Einstein-matter system.