The General Class of Accelerating, Rotating and Charged Plebanski-Demianski Black Holes as Heat Engine

TL;DR

This paper explores the thermodynamics and heat engine potential of the general accelerating, rotating, and charged Plebanski-Demianski black holes in anti-de Sitter space, including stability, phase transitions, and efficiency of thermodynamic cycles.

Contribution

It provides a comprehensive thermodynamic analysis of the general PD black holes, including stability, phase transitions, Joule-Thomson expansion, and heat engine efficiencies, which was not previously studied in detail.

Findings

AdS PD black holes can be thermodynamically stable.

Joule-Thomson expansion indicates heating and cooling regimes.

Maximum efficiency achieved in Carnot and Rankine cycles.

Abstract

We first review the general class of accelerating, rotating and charged Plebanski-Demianski (PD) black holes in presence of cosmological constant, which includes the Kerr-Newman rotating black hole and the Taub-NUT spacetime. We assume that the thermodynamical pressure may be described by the negative cosmological constant and so the black hole represents anti-de Sitter (AdS) PD black hole. The thermodynamic quantities like surface area, entropy, volume, temperature, Gibb's and Helmholtz's free energies of the AdS PD black hole are obtained due to the thermodynamic system. Next we find the critical point and corresponding critical pressure, critical temperature and critical volume for AdS PD black hole. Due to the study of specific heat capacity, we obtain ${\cal C}_{V}=0$ and ${\cal C}_{P}\ge 0$. From this result, we conclude that the AdS PD black hole may be stable. We examine the Joule-Thomson expansion of PD black hole and by evaluating the sign of Joule-Thomson coefficient $\mu$, we determine the heating and cooling nature of PD black hole. Putting $\mu=0$, we find the inversion temperature. Next we study the heat engine for AdS PD black hole. In Carnot cycle, we obtain the work done and its maximum efficiency. Also we describe the work done and its efficiency for a new engine. Finally, we analyze the efficiency for the Rankine cycle in PD black hole heat engine.