The "neighborhood theorem" for the general relativistic characteristic Cauchy problem in higher dimension

TL;DR

This paper proves that in higher-dimensional vacuum Einstein equations, the maximal globally hyperbolic solution around intersecting characteristic hypersurfaces includes a future neighborhood, advancing understanding of the characteristic Cauchy problem in general relativity.

Contribution

It establishes a neighborhood existence result for the characteristic initial-value problem in higher-dimensional vacuum spacetimes, extending previous lower-dimensional results.

Findings

Maximal globally hyperbolic solutions contain a future neighborhood of initial hypersurfaces.

Results apply to higher-dimensional vacuum Einstein equations.

Advances the mathematical understanding of the characteristic Cauchy problem.

Abstract

We show that the maximal globally hyperbolic solution of the initial-value problem for the higher-dimensional vacuum Einstein equations on two transversally intersecting characteristic hypersurfaces contains a future neighborhood of the hypersurfaces.