Sur les corrections de la géométrie thermodynamique des trous noirs

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-Nordström 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-Nordström black holes in the Poincaré patch of $Ad{S}_4$ contains certain narrow range of thermodynamically unstable regions in the statespace. We obtain that the generalized uncertainty principle corrected Ruppenier geometry of Reissner-Nordström 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 $D_1{D}_5$ and $D_2{D}_{6}N{S}_5$ 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.

489 pages, Latex, French, English Abstract

References in corpus (11)

• Near-horizon symmetries of extremal black holes
• The Non-BPS Black Hole Attractor Equation
• On the Thermodynamic Geometry of BTZ Black Holes
• Higher Derivative Corrections to Non-supersymmetric Extremal Black Holes in N=2 Supergravity
• Thermodynamics of charged topological dilaton black holes
• Gravitational Uncertainty and Black Hole Remnants
• Entropy of Reissner-Nordstrom Black Holes with Minimal Length Revisited
• On Attractor Mechanism and Entropy Function for Non-extremal Black Holes/Branes
• Entropy Function for Non-Extremal Black Holes in String Theory
• Determining the Minimal Length Scale of the Generalized Uncertainty Principle from the Entropy-Area Relationship
• Entropy Function for Non-extremal D1D5 and D2D6NS5-branes

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• Geometric Perspective of Entropy Function: Embedding, Spectrum and Convexity
• Thermodynamic Geometry: Evolution, Correlation and Phase Transition
• Intrinsic Geometric Analysis of the Network Reliability and Voltage Stability
• Parameter space stability of multiple soft interactions
• Geometric Design and Stability of Power Networks
• On Intrinsic Geometric Stability of Controller
• On Real Intrinsic Wall Crossings
• A Fluctuation Theory of Topological Susceptibility