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

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 superentropy 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.

Null hypersurface caustics and super-entropic black holes

“…This is in stark contrast to the former patterns of caustics found in Refs. [4,9]. The inspection in this compact paper thus benefits our cognition of the relation between the null hypersurface caustics and the super-entropic state for the black holes.…”

“…Hence, we get our result that the super-entropic accelerating black hole only forms caustic inside the Cauchy horizon of the black hole, being in stark contrast to other super-entropic black holes that develop caustics outside the event horizons mentioned in Refs. [4,9]. 1.…”

“…It was supposed that the emergence of the caustic outside the event horizon may relate to the super-entropy of the ultra-spinning black hole in Ref. [9], where extra ultra-spinning Kerr-Sen-AdS black hole case [10] and ultra-spinning charged BTZ black string case [11] were exemplified.…”

Light Deflection Angle by Superentropic Black Holes

“…More recently, the pulsar SGR J174-2900 near supermassive black holes SgrA* has been explored and investigated providing data on the horizon and the horizonless of events around compact objects [11,12]. A special emphasis has been put on superentropic black holes as fascinate descriptions with non compact horizon topologies having an entropy of maximum bounds [13][14][15][16]. Relaying on certain limits, the superentropic black holes have been approached by considering ultra-spinning limits of the Kerr-Newman-AdS solution [17].…”

Thermodynamic Instability of $\mathrm{3D}$ Einstein-Born-Infeld AdS Black Holes

“…More relevant discussions can be found in refs. [16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”