Coexistent Physics and Microstructure of the Regular Bardeen Black Hole in Anti-de Sitter Spacetime

TL;DR

This paper explores the phase transitions and microscopic interactions of regular Bardeen AdS black holes, revealing distinct microstructure behaviors in small and large black hole phases and analyzing their critical phenomena.

Contribution

It provides a numerical analysis of the phase structure and employs Ruppeiner geometry to uncover microstructure interactions in Bardeen AdS black holes, highlighting differences between small and large black hole phases.

Findings

Small black holes exhibit repulsive microstructure interactions at low temperatures.

Large black holes have attractive microstructure interactions across parameters.

Both phases diverge at the coexistence temperature with a critical exponent of 1/2.

Abstract

We study the phase structure and the microscopic interactions in regular Bardeen AdS black hole. The stable and metastable phases in the black hole are analysed through coexistence and spinodal curves. The solutions are obtained numerically as the analytic solution to the coexistence curve is not feasible. The $P_r-T_r$ coexistence equation is obtained using a fitting formula. The coexistence and spinodal curves are plotted in $P_r-T_r$ and $T_r-V_r$ planes to explore the phase structure of the black hole. In the second part of our study, we were able to probe the microscopic interactions of regular Bardeen AdS black hole using the novel Ruppeiner geometry proposed by S.W. Wei \emph{et.al} Phys. Rev. Lett.123, 071103 (2019). It is found that the microscopic interactions are not same in the small black hole (SBH) and large black hole (LBH) phases. In the SBH phase, there exists a repulsive interaction in the microstructure in the low temperature regime. In contrast, the microstructure associated with the LBH phase has attractive interaction throughout the parameter space. We found that, along the coexistence temperature both the SBH and LBH branches diverge to negative infinity with a critical exponent equal to $1/2$.