Null hypersurface caustics and super-entropic black holes

Abstract

We obtain a charged, rotating and accelerating black hole solution in the f(R) gravity and calculate thermodynamic quantities of the black hole in the slow acceleration regime. We then find that the black hole can be super-entropic in a certain condition. After investigating the null hypersurface of the black hole, we show that there exist super-entropic black holes whose null hypersurface caustics only form inside the Cauchy horizon.