Black Hole Thermodynamics and Riemann Surfaces

Abstract

We use the analytic continuation procedure proposed in our earlier works to study the thermodynamics of black holes in 2+1 dimensions. A general black hole in 2+1 dimensions has g handles hidden behind h horizons. The result of the analytic continuation is a hyperbolic 3-manifold having the topology of a handlebody. The boundary of this handlebody is a compact Riemann surface of genus G=2g+h-1. Conformal moduli of this surface encode in a simple way the physical characteristics of the black hole. The moduli space of black holes of a given type (g,h) is then the Schottky space at genus G. The (logarithm of the) thermodynamic partition function of the hole is the Kaehler potential for the Weil-Peterson metric on the Schottky space. Bekenstein bound on the black hole entropy leads us to conjecture a new strong bound on this Kaehler potential.

17+1 pages, 9 figures

References in corpus (1)

• Analytic Continuation for Asymptotically AdS 3D Gravity

Cited by in corpus (26)

• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Multiboundary Wormholes and Holographic Entanglement
• Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
• Holography and wormholes in 2+1 dimensions
• Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants
• Reconstructing AdS/CFT
• Hot multiboundary wormholes from bipartite entanglement
• Mutual information between thermo-field doubles and disconnected holographic boundaries
• Entanglement entropy in three dimensional gravity
• Binding Complexity and Multiparty Entanglement
• Holographic partition functions and phases for higher genus Riemann surfaces
• Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT
• Islands and mixed states in closed universes
• Behind the geon horizon
• Geometric Microstates for the Three Dimensional Black Hole?
• Handlebody phases and the polyhedrality of the holographic entropy cone
• Tensor Network Models of Multiboundary Wormholes
• BTZ Black Hole Entropy: A spin foam model description
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Holevo Information of Black Hole Mesostates
• The Torus Operator in Holography
• Purely GHZ-like entanglement is forbidden in holography
• Two Splits, Three Ways: Advances in Double Splitting Quenches
• The Riemann Surface of the Logarithm Constructed in a Geometrical Framework
• Hyperthreads in holographic spacetimes
• Numerical Methods for Handlebody Phases