The null-geodesic flow near horizons

TL;DR

This paper analyzes the behavior of null-geodesics near nondegenerate Killing horizons using advanced geometric frameworks, facilitating the study of wave equations in curved spacetime.

Contribution

It applies Vasy and Hintz's framework within Melrose's b-geometry to understand null-geodesic flow near horizons, bridging geometric analysis and wave equation behavior.

Findings

Describes null-geodesic behavior near horizons

Integrates geometric frameworks for wave analysis

Provides tools for linear and nonlinear wave equations

Abstract

This note describes the behavior of null-geodesics near nondegenerate Killing horizons in language amenable to the application of a general framework, due to Vasy and Hintz, for the analysis of both linear and nonlinear wave equations. Throughout, the viewpoint of Melrose's b-geometry on a suitable compactification of spacetime at future infinity is adopted.