Hidden conformal symmetry of the Kerr black hole

Abstract

Extreme and very-near-extreme spin J Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges cL=cR=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 TL=M2/2πJ and TR=√M4−J2 /2πJ. The well-known low-frequency scalar-Kerr 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 Bekenstein-Hawking area law for all M and J. These observations provide evidence for the conjecture that the Kerr black hole is dual to a cL=cR=12J 2D CFT at temperatures (TL,TR) for every value of M and J.