Thermodynamical topology with multiple defect curves for dyonic AdS black holes

TL;DR

This paper explores how multiple defect curves influence the thermodynamical topology of dyonic AdS black holes, revealing stable topological numbers despite complex phase transition behaviors.

Contribution

It uncovers the impact of multiple defect curves on black hole topology and demonstrates the invariance of the topological number amidst complex phase structures.

Findings

Multiple defect curves can occur in black hole topology.

The topological number remains +1 despite multiple defects.

Phase transition regions can be tuned or eliminated by coupling parameters.

Abstract

Dyonic black holes with quasitopological electromagnetism exhibit an intriguing phase diagram with two separated first-order coexistence curves. In this paper, we aim to uncover its influence on the black hole thermodynamical topology. At first, we investigate the phase transition and phase diagram of the dyonic black holes. Comparing with previous study that there is no black hole phase transition region for a middle pressure, we find this region can narrow or disappear by fine tuning the coupling parameter. Instead, two first-order phase transitions can be observed. Importantly, we uncover that such novel phase diagram shall lead to a multiple defect curve phenomenon in black hole topology where each dyonic black hole is treated as one defect in the thermodynamical parameter space. By examining the topology, it is shown that there could be one, three, or five black hole states for given pressure and temperature. For each case, the topological number is calculated. Our results show that the topological number always takes value of +1, keeping unchanged even when the multiple defect curves appear. Therefore, our study provides an important ingredient on understanding the black hole thermodynamical topology.