Charged Rotating Black Hole and the First Law

TL;DR

This paper extends black hole thermodynamics to include charge, demonstrating how charge influences entropy, angular momentum, and the first law, with implications for understanding gravitational systems and their quantum aspects.

Contribution

It introduces a thermodynamic framework for charged rotating black holes, incorporating charge effects into entropy and angular momentum relations, and validates the first law in this context.

Findings

Charge affects the entropy-horizon relationship.

The first law of thermodynamics holds for charged black holes.

Charge effects diminish with distance from the black hole.

Abstract

The thermodynamic properties of black holes have been extensively studied through analogies with classical systems, revealing fundamental connections between gravitation, entropy, and quantum mechanics. In this work, we extend the thermodynamic framework of black holes by incorporating charge and analyzing its role in entropy production. Using an analogy with charged rotating soap bubbles, we demonstrate that charge contributes to the total angular momentum and affects the entropy-event horizon relationship. By applying the Gouy-Stodola theorem, we establish a consistent thermodynamic formulation for charged black holes, showing that the first law of thermodynamics remains valid in this context. Furthermore, we explore the behavior of the partition function from the perspective of a distant observer, revealing that charge effects diminish with increasing distance. These findings reinforce the thermodynamic interpretation of black holes and provide insights into the interplay between charge, rotation, and entropy in gravitational systems.