On thermodynamics of AdS black holes in M-theory

Abstract

Motivated by recent work on asymptotically AdS 4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2-and M5-branes. Concretely, we consider AdS black holes in Ad S p+2 × S 11− p−2 , where p = 2, 5 by interpreting the number of M2-(and M5-branes) as a thermodynamical variable. More precisely, we study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then we compute the thermodynamical curvatures from the Quevedo metric for M2-and M5-branes geometries to reconsider the stability of such black holes. The Quevedo metric singularities recover similar stability results provided by the phase-transition program. It has been shown that similar behaviors are also present in the limit of large N .

On thermodynamics of charged AdS black holes in extended phases space via M2-branes background

“…(1) can be interpreted as the near horizon geometry of N coincident configurations of M2-branes. In this background, the AdS radius L is linked to the M2-brane number N via the relation [1,34,37,38]…”

“…According to the proposition reported in [1,[20][21][22], we consider the cosmological constant as the number of M2-branes in the M-theory background and its conjugate quantity as the associated chemical potential.…”

“…To close this section as in [1], we learn that one can associate the singularities of the C φ,N with the poles of the Weinhold and Ruppeiner scalar curvatures metrics, while the divergences of C Q,N correspond exactly to the singular points of the curvature of Quevedo metric.…”

“…All these recent inspiring works on asymptotically AdS 4 black holes in M-theory [28][29][30][31][32] motivate us to study the thermodynamics and thermodynamical geometry of Ad S 4 × S 7 , from the physics of M2-branes, where we interpret the number of M2-branes as a thermodynamical variable as in [1]. We then discuss the stability of such solutions and examine the corresponding first phase transition by analyzing various relevant quantities including the chemical potential, free energy, and heat capacities.…”

$$P$$ P – $$V$$ V criticality of AdS black hole in the Einstein–Maxwell–power-Yang–Mills gravity

“…This analogy becomes more natural in this extended phase space. Until now, these critical behaviour of a lot of black hole systems in this extended phase space are under discussion in this direction [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. It is worth to noting that, in four-dimensional Born-Infeld AdS black holes [4], the impact of the nonlinearity can bring the new phenomenon of reentrant phase transition which was observed in rotating AdS holes [19,20], while this reentrant phase transition does not occur for higher dimensional Born-Infeld AdS black holes [21].…”