The extended phase space thermodynamics of Planck-scale-corrected Reissner-Nordstr\"om-anti-de Sitter black hole

TL;DR

This paper investigates how Planck-scale modifications to the radiation equation of state influence the thermodynamics, phase transitions, and heat engine cycles of Reissner-Nordström-anti-de Sitter black holes, revealing notable differences between correction types.

Contribution

It introduces a detailed analysis of Planck-scale corrections on black hole thermodynamics, highlighting differences between linear and quadratic modifications.

Findings

Deformed thermodynamic quantities are derived.

Phase transition behaviors are characterized.

Black holes as heat engines are analyzed for different cycles.

Abstract

We analyze the effect of Planck-scale modified radiation equation of state on the Reissner-Nodstr\"om-anti-de Sitter black hole inspired by Kiselev's ansatz. Deformed thermodynamic quantities are found, phase transitions and black holes as heat engines are described for the Carnot and square cycles. Non-trivial differences between linear and quadratic Planck-scale corrections are discussed in detail.