Hidden Conformal Symmetry of the Kerr Black Hole

TL;DR

This paper provides evidence that Kerr black holes exhibit a hidden conformal symmetry at low frequencies, suggesting a duality with a 2D conformal field theory for all spin and mass values, not just in the extreme case.

Contribution

It demonstrates the persistence of conformal symmetry in scalar wave equations for non-extreme Kerr black holes and links scattering amplitudes to 2D CFT correlators.

Findings

Conformal symmetry persists for generic Kerr black holes at low frequencies.

Scalar scattering amplitudes match 2D CFT correlators at specific temperatures.

CFT microstate count agrees with Bekenstein-Hawking entropy for all parameters.

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 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 non-extreme values of the mass M. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The periodic identification of the azimuthal angle is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures (T_L,T_R). 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 c_L=c_R=12J 2D CFT at temperatures (T_L,T_R) for every value of M and J.