Schwarzschild horizon dynamics and SU(2) Chern-Simons theory

Abstract

We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invariance, on the description of the horizon degrees of freedom of a Schwarzschild black hole as an SU(2) Chern-Simons theory with specific sources. A classically equivalent description in terms of an ISO(2) Chern-Simons theory is also discussed. Further, we demonstrate that both these descriptions can be partially gauge fixed to a horizon theory with U(1) local gauge invariance, with the solder form sources being subject to extra constraints in directions orthogonal to an internal vector field left invariant by U(1) transformations. Seemingly disparate approaches on characterization of the horizon theory for the Schwarzschild black hole (as well as spherical Isolated Horizons in general) are thus shown to be equivalent physically.

22 pages Latex, no figures, version accepted for publication in Physical Review D

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• Quantum Hairs and Entropy of Quantum Isolated Horizon from Chern-Simons Theory
• A Note on Black Hole Entropy in Loop Quantum Gravity
• Local symmetries of non-expanding horizons
• Black-hole horizons in modified space-time structures arising from canonical quantum gravity
• Thermal stability of black holes with arbitrary hairs
• Thermal Fluctuations And Correlations Among Hairs Of Stable Quantum ADS Kerr-Newman Black Hole
• A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies
• Four-Dimensional Entropy from Three-Dimensional Gravity
• Stability of Quantum Isolated Horizon : A Local Observer's View
• Effective field theory description of horizon-fluid determines the scrambling time
• Thermodynamic partition function from quantum theory for black hole horizons in loop quantum gravity
• Can Gravitational Wave Data Shed Light on Dark Matter Particles ?
• Note on $SU(2)$ isolated horizon