Null hypersurface caustics, closed null curves, and super entropy

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 Baiiados-Teitelboim-Zanelli (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.

Automated summary

This study explores the development of super-entropic black holes and NHC in certain black hole spacetimes. The relationship between super-entropic black holes, NHC, and closed causal curves is complex and not straightforward. Examples, such as the BTZ black string, demonstrate that even non-super-entropic spacetimes can have NHC outside the horizon.