Null hypersurface caustics and super-entropic black holes

TL;DR

This paper derives a charged, rotating, accelerating black hole solution in f(R) gravity, explores its thermodynamics, identifies conditions for super-entropic behavior, and analyzes null hypersurface caustics, revealing they form inside the Cauchy horizon.

Contribution

It presents a new black hole solution in f(R) gravity and investigates its thermodynamic and geometric properties, including super-entropic conditions and caustic formation.

Findings

Black hole can be super-entropic under certain conditions.

Null hypersurface caustics form only inside the Cauchy horizon.

Thermodynamic quantities are calculated in the slow acceleration regime.

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.