On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations

TL;DR

This paper establishes the existence of solutions for a class of nonlinear symmetric hyperbolic systems, including Einstein equations, with initial data on intersecting null surfaces, advancing understanding of characteristic initial value problems.

Contribution

It proves the existence of solutions for symmetric hyperbolic systems with null initial data, including Einstein equations, on a future neighborhood of initial surfaces.

Findings

Existence of solutions for symmetric hyperbolic systems with null initial data.

Application to Einstein equations and semilinear wave equations.

Framework for characteristic initial value problems in general relativity.

Abstract

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the initial surfaces. The general result is applied to general semilinear wave equations, as well as the Einstein equations with or without sources, and conformal variations thereof.