Relativistic Lagrange Formulation

TL;DR

This paper introduces a generalized Lagrange formulation applicable to various PDE systems, including those in general relativity, and proves that initial-value formulations are preserved under this transformation.

Contribution

It presents a new generalized Lagrange formulation for PDE systems and proves its compatibility with initial-value problems, extending classical fluid dynamics concepts.

Findings

Generalized Lagrange formulation applicable to diverse PDE systems

Preservation of initial-value formulation under the new framework

Applicability to systems in general relativity

Abstract

It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial differential equations. These include numerous systems of physical interest, in particular, those for various material media in general relativity. There is proved a key theorem, to the effect that, if the original (Euler) system admits an initial-value formulation, then so does its generalized Lagrange formulation.