Entropy Bound of Horizons for Accelerating, Rotating and Charged Plebanski-Demianski Black Hole

TL;DR

This paper investigates the thermodynamic properties and entropy bounds of the complex Plebanski-Demianski black hole, which includes various known black hole solutions, revealing that many horizon products depend on black hole parameters and are not universal.

Contribution

It provides a detailed analysis of entropy, area bounds, and thermodynamic relations for the Plebanski-Demianski black hole, including new results on horizon products and extremal mass.

Findings

Entropy and area products depend on black hole parameters.

Derived bounds for entropy and area of horizons.

Established thermodynamic relations and extremal mass for PD black hole.

Abstract

We first review the accelerating, rotating and charged Plebanski-Demianski (PD) black hole, which includes the Kerr-Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product are found for event horizon and Cauchy horizon. Also their sums are also found for both horizons. All these relations are found to be depend on mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons are investigated. Also we found the Christodoulou-Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.