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

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 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.

The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss-Bonnet gravity: from the critical point to the triple point

“…In particular, the critical phenomena are observed for the normalized curvature scalar reflecting a universal property of the Ruppeiner geometry. Such study has also been extended to other black hole systems and much more interesting results were obtained [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

General thermodynamic geometry approach for rotating Kerr anti-de Sitter black holes

“…By using the Christodoulou-Ruffini-like squared-mass formula (13), we can calculate the scalar curvature through (40). The non-vanishing components of the metric are given by…”

“…The approach has also been generalized to other black hole backgrounds [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. For the neutral AdS black hole, we constructed its Ruppeiner geometry, and found that there is only the attractive interaction for arbitrary spacetime dimension.…”

Connections between entropy surface density and microscopic property in black holes

“…where M is black hole mass, g 1 magnetic charge, q electric charge, and g 2 integration constant related to magnetic charges or simply regarded as [45] magnetic charge. The entropy and event horizon area of the three regular black holes take [31,34,35] the forms, ‡ respectively,…”

“…As is well known, many black holes in Einstein's gravity satisfy the famous Bekenstein-Hawking entropy relation, that is, S = A/4, where A is event horizon area. However, it is not valid [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], for instance, in regular black holes [39][40][41] and Gauss-Bonnet black holes [27,28,42,43], where the former is a kind of black holes without spacetime singularity and the latter a special kind of black holes in Lovelock gravity theory with higher-order curvature corrections. This phenomenon indicates that the entropy surface density, σ S ≡ S/A, of regular black holes and Gauss-Bonnet black holes is not a constant 1/4, but a function of event horizons, and that the entropy surface density of regular and Gauss-Bonnet black holes may be a non-trivial physical quantity.…”