Null Hypersurface Caustics, Closed Null Curves, and Super-Entropy

TL;DR

This paper investigates the development of null hypersurface caustics outside black hole horizons, especially in super-entropic and other exotic spacetimes, revealing complex relationships between caustics, closed null curves, and super-entropy.

Contribution

It extends the study of null hypersurface caustics to various black hole spacetimes, highlighting their occurrence beyond the horizon and their relation to closed null curves and super-entropy.

Findings

Exterior caustics can develop in multiple black hole spacetimes.

Presence of closed null curves coincides with caustics in some cases.

Super-entropic black holes can have exterior caustics without closed null curves.

Abstract

Recently it was discovered that null hypersurfaces can develop caustics outside the event horizon of super-entropic Kerr-AdS black holes, in contrast to the usual Kerr-AdS case. In this work we explore a few more examples of black hole spacetimes in which such exterior caustics can develop. If a closed null curve is present, e.g., in the case of Taub-NUT and the "transunital" Kerr-AdS spacetimes, then it coincides with a null hypersurface caustic (NHC) of a minimal separation parameter. Thus a spacetime on the verge of forming closed timelike curves could develop a caustic. Known examples of super-entropic black holes also have exterior NHC, although such spacetimes are free of closed null/timelike curves. Nevertheless the relationship between closed causal curves, NHC, and super-entropy is not straightforward. This is best illustrated with the BTZ black string, which for some choices of the warp factor in the extra dimension and the value of the charge, can be super-entropic. However, even those that are not super-entropic can admit NHC outside the horizon.