Van der Waals Black Holes: Universality, Quantum Corrections, and Topological Classifications

TL;DR

This paper studies Van der Waals black holes' thermodynamics, quantum corrections, and topological classifications, revealing universal relations and stability features across different quantum frameworks.

Contribution

It introduces a unified analysis of Van der Waals black holes' thermodynamic topology under quantum corrections, highlighting the robustness and classification changes due to various quantum effects.

Findings

Universal extremality relation persists with quantum corrections.

Topological charges vary with parameters, indicating different stability regimes.

Quantum corrections influence topological classifications and stability.

Abstract

In this paper, we investigate the universal extremality relation and thermodynamic topology of Van der Waals (VdW) black holes-solutions of Einstein's equations whose thermodynamic behavior closely resembles that of Van der Waals fluids. In the classical case, the black hole entropy obeys the Bekenstein-Hawking area law and satisfies the standard universality relation. We then incorporate quantum corrections using three distinct frameworks: the Generalized Uncertainty Principle (GUP), the Extended Uncertainty Principle (EUP), and Rainbow Gravity. While these corrections modify the entropy law, we find that a generalized form of the universal extremality relation still holds. Next, we explore the thermodynamic topology of VdW black holes, focusing on the distribution of topological charges. Our analysis reveals that variations in the black hole and model parameters lead to significant changes in topological classifications and stability, as quantified by winding numbers. In the GUP-corrected case, topological charge distributions exhibit robustness against parameter variations, suggesting classification stability. For EUP-corrected black holes, we identify two distinct topological classes, with some configurations displaying three non-zero topological charges and others maintaining a total charge of zero, despite changes in individual charge counts. The Rainbow Gravity-corrected scenario shows similar consistency in topological behavior.