Sur les corrections de la g\'eom\'etrie thermodynamique des trous noirs

TL;DR

This paper investigates the thermodynamic geometry of various black holes and branes, analyzing stability, interactions, and the effects of stringy and quantum corrections on their state space geometries.

Contribution

It provides a comprehensive analysis of the thermodynamic geometries of black holes with corrections, revealing stability properties and the impact of stringy and quantum effects.

Findings

Reissner-Nordström black holes have well-defined Ruppenier geometry indicating non-interacting systems.

Large mass Reissner-Nordström black holes in AdS have unstable regions in their state space.

Stringy α'-corrections do not introduce singularities in extremal black hole geometries.

Abstract

We study thermodynamic geometry of certain black holes and black branes with and without generalized uncertainty principle or stringy $ \alpha^{\prime} $-corrections to the entropy. From this perspective, we analyze Ruppenier geometry of Reissner-Nordstr\"om black holes and show that it is well defined and corresponds to a non-interacting statistical system. We investigate that the Weinhold geometry of dilatonic black holes is regular everywhere and that of large mass Reissner-Nordstr\"om black holes in the Poincar\'e patch of $ AdS_4 $ contains certain narrow range of thermodynamically unstable regions in the statespace. We obtain that the generalized uncertainty principle corrected Ruppenier geometry of Reissner-Nordstr\"om black holes correspond to a non-interacting statistical system unlike the magnetically charged black holes. We show that the stringy $ \alpha^{\prime} $-corrections do not introduce singularity in the statespace geometry of non-supersymmetric extremal black holes in $ D= 4 $. Interestingly, the degree of scalar curvature and that of the determinant of this Ruppenier geometry can be written as an integer multiple of the order of $ \alpha^{\prime} $-correction. We further show that the statespace geometry of Gauss- Bonnet corrected supersymmetric extremal black holes in $ D=4 $ as well as non-extremal $D_1D_5$ and $D_2D_6NS_5$ black branes in $ D=10 $ is regular everywhere. Furthermore, the thermodynamic geometry of four dimensional rotating Kerr-Newman extremal black holes in Einstein-Maxwell theory is everywhere ill-defined and that of the Kaluza-Klein black holes in Einstein-Maxwell theory or the one arrising from heterotic string compactification is ill-defined only at the points of the ergo-branch.