Uniqueness results for ill posed characteristic problems in curved space-times

TL;DR

This paper establishes two uniqueness theorems for solutions of wave equations on characteristic hypersurfaces, one in Minkowski space and the other on a Kerr black hole's event horizon, addressing ill-posed problems.

Contribution

It provides the first known uniqueness results for ill-posed characteristic problems in curved space-times, including Kerr black holes.

Findings

Uniqueness theorems for linear and nonlinear wave equations on characteristic hypersurfaces.

Results apply to Minkowski space and Kerr black hole horizons.

Addresses ill-posed Cauchy problems in curved space-times.

Abstract

We prove two uniqueness theorems for solutions of linear and nonlinear wave equations; the first theorem is in the Minkowski space while the second is in the domain of outer communication of a Kerr black hole. Both theorems concern ill posed Cauchy problems on smooth, bifurcate, characteristic hypersurfaces. In the case of the Kerr space-time this hypersurface is the event horizon of the black hole.