# 4D-EGB Black Holes in RPS Thermodynamics

## TL;DR

This paper explores the thermodynamics of 4D Einstein-Gauss-Bonnet black holes within the restricted phase space framework, revealing how the Gauss-Bonnet term influences phase transitions and black hole properties.

## Contribution

It introduces a conjugate quantity for the Gauss-Bonnet parameter in the RPST formalism and analyzes its impact on black hole thermodynamics and phase transitions.

## Key findings

- Gauss-Bonnet term affects black hole thermodynamics and phase behavior.
- Uncharged black holes exhibit effective charge behavior due to Gauss-Bonnet.
- Hawking-Page transition occurs between large black holes and thermal AdS space.

## Abstract

In this paper, we study thermodynamics of charged and uncharged 4-Dimension Einstein-Gauss-Bonnet (4D-EGB) black holes. The context of this study is the Visser's holographic thermodynamics with a fixed anti-de Sitter radius and a variable Newton constant known as restricted phase space thermodynamics (RPST). Our setup is constructed by using the AdS/CFT correspondence and by introducing a conjugate quantity of the Gauss-Bonnet parameter. By this ansatz, we conclude that the Gauss-Bonnet action multiplied by a temperature, behaves as a free energy. We derive the conjugate quantities corresponding to the first law in the RPST formalism. The study of the $T-S$ processes and the effect of the Gauss-Bonnet constant, $\alpha$, show that thermodynamic properties of charged black holes depend on the Gauss-Bonnet term and the charge of black holes. For an uncharged black holes, the effect of Gauss-Bonnet becomes crucial, as it behaves as a charged black hole with an effective charge. Finally, we find that the Hawking-Page phase transition occurs between a large black hole and a thermal AdS space.