Smooth null hypersurfaces near the horizon in the presence of tails

TL;DR

This paper demonstrates that tail decay modes in linear black hole perturbations do not cause caustics on certain null surfaces near the horizon, clarifying the geometric behavior of perturbations.

Contribution

It shows that tail modes do not generate caustics on null surfaces near the horizon, improving understanding of black hole perturbation geometry.

Findings

Tail modes do not produce caustics near the horizon.

Null surfaces remain regular despite tail decay.

Provides insight into black hole perturbation behavior.

Abstract

We show that the power-law decay modes found in linear perturbations of Schwarzschild black holes, generally called tails, do not produce caustics on a naturally defined family of null surfaces in the neighborhood of i+ of a black hole horizon.