Lagrange coordinates for the Einstein-Euler equations

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.

References in corpus (3)

• Well posedness for the motion of a compressible liquid with free surface boundary
• Boundary conditions for coupled quasilinear wave equations with application to isolated systems
• Well-posedness of compressible Euler equations in a physical vacuum

Cited by in corpus (4)

• A priori estimates for relativistic liquid bodies
• Localized big bang stability for the Einstein-scalar field equations
• Hamilton-Jacobi hydrodynamics of pulsating relativistic stars
• Development of singularities in the relativistic Euler equations