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

Understand

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.