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.
Highlights
The well-known vacuum C-metric was introduced in Refs. [1,2] and investigated in Refs. [3,4]
The C-metric is a solution of the Einstein(-Maxwell) field equations; physically, it can be interpreted as two uniformly accelerating black holes dragged by forces originating from conical singularities [6]
In contrast to the flat or de Sitter C-metrics, the anti-de Sitter (AdS) C-metric can describe a pair of accelerated black holes only when the acceleration parameter A and the AdS radius l satisfy a certain restriction, originally thought to be A > 1=l [10]
Summary
The well-known vacuum C-metric was introduced in Refs. [1,2] and investigated in Refs. [3,4]. An explication of the thermodynamic parameters of accelerating AdS black holes with charge and rotation was studied in [17], and these results were used to obtain a remarkable snapping-swallowtail phase transition for the charged case at a certain pressure [18]. We obtain charged accelerating black hole solutions in fðRÞ gravity and study their thermodynamics. The thermodynamics of charged black holes in fðRÞ gravity have been studied previously [27], and phase transitions analogous to the van der Waals liquid-gas system between small and large black holes were observed.
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