Hidden conformal symmetry of the Kerr black hole
Abstract
Extreme and verynearextreme spin J Kerr black holes have been conjectured to be holographically dual to twodimensional (2D) conformal field theories (CFTs) with left and right central charges c_{L}=c_{R}=12J. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic nonextreme values of the mass M≠J. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The 2π periodic identification of the azimuthal angle ϕ is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures T_{L}=M^{2}/2πJ and T_{R}=M^{4}J^{2}/2πJ. The wellknown lowfrequency scalarKerr scattering amplitudes coincide with correlators of a 2D CFT at these temperatures. Moreover, the CFT microstate degeneracy inferred from the Cardy formula agrees exactly with the BekensteinHawking area law for all M and J. These observations provide evidence for the conjecture that the Kerr black hole is dual to a c_{L}=c_{R}=12J 2D CFT at temperatures (T_{L},T_{R}) for every value of M and J.
 Publication:

Physical Review D
 Pub Date:
 July 2010
 DOI:
 10.1103/PhysRevD.82.024008
 arXiv:
 arXiv:1004.0996
 Bibcode:
 2010PhRvD..82b4008C
 Keywords:

 04.70.Dy;
 04.70.Bw;
 Quantum aspects of black holes evaporation thermodynamics;
 Classical black holes;
 High Energy Physics  Theory
 EPrint:
 17 pages