Thermodynamic curvature and black holes

Abstract

I give a relatively broad survey of thermodynamic curvature $R$, one spanning results in fluids and solids, spin systems, and black hole thermodynamics. $R$ results from the thermodynamic information metric giving thermodynamic fluctuations. $R$ has a unique status in thermodynamics as being a geometric invariant, the same for any given thermodynamic state. In fluid and solid systems, the sign of $R$ indicates the character of microscopic interactions, repulsive or attractive. $|R|$ gives the average size of organized mesoscopic fluctuating structures. The broad generality of thermodynamic principles might lead one to believe the same for black hole thermodynamics. This paper explores this issue with a systematic tabulation of results in a number of cases.

27 pages, 10 figures, 7 tables, 78 references. Talk presented at the conference Breaking of Supersymmetry and Ultraviolet Divergences in extended Supergravity, in Frascati, Italy, March 27, 2013. v2 corrects some small problems

References in corpus (6)

• Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Geometrothermodynamics of black holes
• Nonperturbative Thermodynamic Geometry of Anyon Gas
• A Commentary on Ruppeiner Metrics for Black Holes
• Thermodynamic geometry of a kagome Ising model in a magnetic field

Cited by in corpus (65)

• Ruppeiner Geometry, Phase Transitions, and the Microstructure of Charged AdS Black Holes
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• Black holes and Boyle's law -- the thermodynamics of the cosmological constant
• Ruppeiner thermodynamic geometry for the Schwarzschild-AdS black hole
• On thermal molecular potential among micromolecules in charged AdS black holes
• Geometrical thermodynamics and P-V criticality of the black holes with power-law Maxwell field
• Microscopic structures and thermal stability of black holes conformally coupled to scalar fields in five dimensions
• Thermodynamics of charged accelerating AdS black holes and holographic heat engines
• Accelerating AdS black holes as the holographic heat engines in a benchmarking scheme
• Parametric phase transition for Gauss-Bonnet AdS black hole
• Ruppeiner Geometry, Reentrant Phase transition and Microstructure of Born-Infeld AdS Black Hole
• Microstructure of charged AdS black hole via $P-V$ criticality
• Thermodynamics, phase transitions and Ruppeiner geometry for Einstein-dilaton Lifshitz black holes in the presence of Maxwell and Born-Infeld electrodynamics
• Quasi-homogeneous black hole thermodynamics
• Interaction potential and thermo-correction to the equation of state for thermally stable Schwarzschild Anti-de Sitter black holes
• Fokker-Planck equation for black holes in thermal potential
• Phase transition and microstructures of five-dimensional charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble
• Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity
• Thermodynamic stability of asymptotically anti-de Sitter rotating black holes in higher dimensions
• The intrinsic curvature of thermodynamic potentials for black holes with critical points
• Microscopic explanation for black hole phase transitions via Ruppeiner geometry: two competing factors-the temperature and repulsive interaction among BH molecules
• The correspondence between thermodynamic curvature and isoperimetric theorem from ultraspinning black hole
• van der Waals fluid and charged AdS black hole in the Landau theory
• Phase transition and thermodynamic geometry of $f(R)$ AdS black holes in the grand canonical ensemble
• Homogeneity and thermodynamic identities in geometrothermodynamics
• Diagnosis inspired by the thermodynamic geometry for different thermodynamic schemes of the charged BTZ black hole
• Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes
• Weinhold geometry and thermodynamics of Bardeen AdS black holes
• Thermodynamics curvature in phase transitions for AdS black hole
• Some Early Ideas on the Metric Geometry of Thermodynamics
• Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly
• Thermodynamic Metrics and Black Hole Physics
• Comment on "Insight into the Microscopic Structure of an AdS Black Hole from a Thermodynamical Phase Transition"
• Infinitesimal Legendre symmetry in the Geometrothermodynamics programme
• Black String in Massive Gravity
• Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition
• Dynamic Property of Phase Transition for Non-Linear Charged Anti-de Sitter black holes
• Superconducting phase transition reveals an electromagnetic coupling to a scalar field potential that generates mechanical work
• Cosmological FLRW phase transitions and micro-structure under Kaniadakis statistics
• Thermodynamic metric geometry of the two-state ST2 model for supercooled water
• Non-extended phase space thermodynamics of Lovelock AdS black holes in grand canonical ensemble
• Thermodynamic geometry and phase transition of spinning AdS black holes
• Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space
• On the microstructure of higher-dimensional Reissner-Nordström black holes in quantum regime
• Phase transition of non-linear charged Anti-de Sitter black holes
• Exploring the Effects of Generalized Entropy onto Bardeen Black Hole Surrounded by Cloud of Strings
• Overview of thermodynamic properties for Reissner-Nordstrom-de Sitter spacetime in induced phase space
• Can we know about black hole thermodynamics through shadows?
• The Hookean Law of Black Holes and Fragmentation: Insights from Maximum Force Conjecture and Ruppeiner Geometry
• Can shadows connect black hole microstructures?
• Geometrothermodynamic cosmology
• Geometrothermodynamic model for the evolution of the Universe
• A new measure of thermal micro-behavior for the AdS black hole
• Geometrothermodynamics of black hole binary systems
• Thermodynamic geometry for a non-extensive ideal gas
• Unitary thermodynamics from thermodynamic geometry II: Fit to a local density approximation
• Insight into the Microscopic Structure of an AdS Black Hole from the Quantization
• Generalised complex geometry in thermodynamical fluctuation theory
• Thermodynamics of Charged Lovelock - AdS Black Holes
• Black Holes and Thermogeometric Optimization
• Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy
• Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising Chains
• Connections between entropy surface density and microscopic property in black holes
• Thermodynamic aspects of FLRW Universe in Einstein-Gauss-Bonnet domains