Black hole entropy and SU(2) Chern-Simons theory.

Black holes (BH's) in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with punctures. Remarkably, when considering an ensemble of fixed horizon area a(H), the counting can be mapped to simply counting the number of SU(2) intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to a(H) with logarithmic corrections ΔS=-3/2 loga(H). Our treatment from first principles settles previous controversies concerning the counting of states.

[1]  Quantum black holes: Entropy and entanglement on the horizon , 2005, gr-qc/0508085.

[2]  Eduardo J S Villaseñor,et al.  Black hole state counting in loop quantum gravity: a number-theoretical approach. , 2008, Physical review letters.

[3]  Algebraic approach to quantum black holes: Logarithmic corrections to black hole entropy , 2002, gr-qc/0210024.

[4]  G. J.FernandoBarbero,et al.  On the computation of black hole entropy in loop quantum gravity , 2008, Classical and Quantum Gravity.

[5]  A. Ashtekar,et al.  Quantum geometry and black hole entropy , 1998 .

[6]  S. Carlip,et al.  Logarithmic corrections to black hole entropy, from the Cardy formula , 2000 .

[7]  Edward Witten,et al.  Quantum field theory and the Jones polynomial , 1989 .

[8]  G. J.FernandoBarbero,et al.  Combinatorics of the SU(2) black hole entropy in loop quantum gravity , 2009, 0906.4529.

[9]  Quantum geometry of isolated horizons and black hole entropy , 2000, gr-qc/0005126.

[10]  Generating functions for black hole entropy in loop quantum gravity , 2008, 0804.4784.

[11]  Rovelli.  Black Hole Entropy from Loop Quantum Gravity. , 1996, Physical review letters.

[12]  R. Wald,et al.  Local symmetries and constraints , 1990 .

[13]  S. Hawking.  Particle creation by black holes , 1975 .

[14]  Linking topological quantum field theory and nonperturbative quantum gravity , 1995, gr-qc/9505028.

[15]  Majumdar,et al.  Logarithmic correction to the bekenstein-hawking entropy , 2000, Physical review letters.

[16]  A. Ashtekar,et al.  Isolated horizons: The classical phase space , 1999, Advances in Theoretical and Mathematical Physics.