Quasi-Spherical Light Cones of the Kerr Geometry

TL;DR

This paper studies quasi-spherical light cones in Kerr spacetime, showing they are caustic-free and useful for wave propagation, coordinate systems, and initial-value problems around spinning black holes.

Contribution

It develops the equations for quasi-spherical light cones in Kerr geometry and analyzes their properties, including caustic avoidance.

Findings

Light cones are caustic-free for all positive Kerr radial coordinates.

The surfaces are asymptotic to Minkowski light cones at infinity.

Applications include wave propagation and coordinate system definitions.

Abstract

Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We develop the equations of these surfaces and examine their properties. In particular, we show that they are free of caustics for all positive values of the Kerr radial coordinate r. Useful applications include the propagation of high-frequency waves, the definition of Kruskal-like coordinates for a spinning black hole and the characteristic initial-value problem.