Lagrange coordinates for the Einstein-Euler equations

TL;DR

This paper introduces a new symmetric hyperbolic formulation of the Einstein-Euler equations in Lagrange coordinates, linking coordinate systems with a fictitious fluid model, enhancing mathematical and physical understanding.

Contribution

It develops a novel symmetric hyperbolic formulation of Einstein-Euler equations in Lagrange coordinates, connecting coordinate choices with fluid models.

Findings

Lagrange coordinates are equivalent to densitized lapse and zero shift systems for vacuum Einstein equations.

The formulation provides a new perspective on the Einstein-Euler system.

Application to vacuum Einstein equations demonstrates the utility of the new coordinates.

Abstract

We derive a new symmetric hyperbolic formulation of the Einstein-Euler equations in Lagrange coordinates that are adapted to the Frauendiener-Walton formulation of the Euler equations. As an application, we use this system to show that the densitized lapse and zero shift coordinate systems for the vacuum Einstein equations are equivalent to Lagrange coordinates for a fictitious fluid with a specific equation of state.