# Charged accelerating black hole in $f(R)$ gravity

## TL;DR

This paper derives a charged accelerating AdS black hole solution in $f(R)$ gravity, explores its thermodynamics, and generalizes the reverse isoperimetric inequality, revealing super-entropic properties.

## Contribution

It introduces a new charged accelerating black hole solution in $f(R)$ gravity and extends thermodynamic and geometric inequalities to this context.

## Key findings

- Black hole solutions without acceleration horizons in $f(R)$ gravity.
- Generalization of the reverse isoperimetric inequality for $f(R)$ black holes.
- Black holes can be super-entropic compared to Einstein gravity counterparts.

## Abstract

We obtain a charged accelerating AdS black hole solution in $f(R)$ gravity and investigate its thermodynamic behaviour. We consider low-acceleration black holes that do not have an acceleration horizon and obtain the first law of thermodynamics for them. We further study the parameter space of charged slowly accelerating $f(R)$ AdS black holes before investigating the behaviour of the free energy in both the canonical and grand canonical ensembles. We find a generalization of the reverse isoperimetric inequality, applicable to black holes in $f(R)$ gravity, that indicates these black holes can become super-entropic relative to their counterparts in Einstein gravity.