Global regular null hypersurfaces in a perturbed Schwarzschild black hole exterior

TL;DR

This paper proves the existence of non-spherically symmetric, regular null hypersurface foliations in perturbed Schwarzschild black hole exteriors, relaxing symmetry and differentiability conditions.

Contribution

It extends the theory of null hypersurfaces to more general, less symmetric, and less smooth perturbed Schwarzschild spacetimes, showing such foliations still exist.

Findings

Existence of non-spherical null hypersurface foliations

Null hypersurfaces extend regularly to past null infinity

Results hold under relaxed differentiability conditions

Abstract

The spherically symmetric null hypersurfaces in a Schwarzschild spacetime are smooth away from the singularities and foliate the spacetime. We prove the existence of more general foliations by null hypersurfaces without the spherical symmetry condition. In fact we also relax the spherical symmetry of the ambient spacetime and prove a more general result: in a perturbed Schwarzschild spacetime (not necessary being vacuum), nearly round null hypersurfaces can be extended regularly to the past null infinity, thus there exist many foliations by regular null hypersurfaces in the exterior region of a perturbed Schwarzschild black hole. A significant point of the result is that the ambient spacetime metric is not required to be differentiable in all directions.