Thermodynamics of Charged AdS Black Holes in Extended Phases Space via M2-branes Background

TL;DR

This paper explores the thermodynamics and stability of charged AdS black holes in M-theory with M2-branes, analyzing phase transitions and thermodynamical geometries to understand their physical behavior.

Contribution

It introduces a detailed thermodynamic analysis of AdS black holes in M2-branes background, including thermodynamical geometry, which is a novel approach in this context.

Findings

Singularities in thermodynamical curvature metrics match phase transition points.

Stability behaviors are consistent across different thermodynamic ensembles.

Results recover known cases when the charge vanishes.

Abstract

Motivated by a recent work on asymptotically Ad$S_4$ black holes in M-theory, we investigate both thermodynamics and thermodynamical geometry of Raissner-Nordstrom-AdS black holes from M2-branes. More precisely, we study AdS black holes in $AdS_{4}\times S^{7}$, with the number of M2-branes interpreted as a thermodynamical variable. In this context, we calculate various thermodynamical quantities including the chemical potential, and examine their phase transitions along with the corresponding stability behaviors. In addition, we also evaluate the thermodynamical curvatures of the Weinhold, Ruppeiner and Quevedo metrics for M2-branes geometry to study the stability of such black object. We show that the singularities of these scalar curvature's metrics reproduce similar stability results obtained by the phase transition program via the heat capacities in different ensembles either when the number of the M2 branes or the charge are held fixed. Also, we note that all results derived in [1] are recovered in the limit of the vanishing charge.