Thermal chaos of quantum-corrected-AdS black hole in the extended phase space

TL;DR

This paper investigates the thermodynamic and chaotic behavior of quantum-corrected Schwarzschild-like black holes in extended phase space, revealing how quantum corrections influence chaos across different universe models.

Contribution

It introduces an analysis of thermal chaos in quantum-corrected black holes using the Melnikov method, highlighting the impact of quantum corrections on chaos likelihood in various universe geometries.

Findings

Black hole thermodynamics resemble Van der Waals systems.

Quantum correction parameter affects chaos likelihood.

Chaos is more difficult in open universes with specific parameters.

Abstract

We briefly analyzed the equation of state and critical points of the quantum-corrected Schwarzschild-like black hole and used the Melnikov method to study its thermal chaotic behavior in the extended phase space of flat, closed, and open universes. The results show that the black hole's thermodynamic behavior is similar to that of the Van der Waals system. Although the critical ratios at the critical points differ among the three universes, they are all independent of the quantum correction parameter. For chaos, time perturbations will lead to chaotic behavior when their amplitude exceeds a critical value that depends on the quantum correction parameter and the radius of the dust sphere in the FRW model. Based on this, we found that the chaotic behavior of the black hole varies across different universes depending on the quantum correction parameter, but this parameter always makes chaos more likely. Using the value of the quantum correction parameter determined by Meissner, chaos is always more difficult to occur in an open universe compared to the other two types of universes. Which universe is most prone to chaos depends on the radius of the dust sphere. Finally, chaotic behavior is always present under spatial perturbations.