Hidden Conformal Symmetry of the Kerr Black Hole

By A. Castro, A. Maloney, Andrew Strominger. 2010

332 citations recorded by the source corpus.

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 nonextreme values of the mass $M\ensuremath{\ne}\sqrt{J}$. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The $2\ensuremath{\pi}$ periodic identification of the azimuthal angle $\ensuremath{\phi}$ is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures ${T}_{L}={M}^{2}/2\ensuremath{\pi}J$ and ${T}_{R}=\sqrt{{M}^{4}\ensuremath{-}{J}^{2}}/2\ensuremath{\pi}J$. 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 $J$.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/262716530789a546b6908eae8df8d895a2381e11

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Citations in the corpus

Static patch solipsism: conformal symmetry of the de Sitter worldline (2011, background): “Such a hidden conformal symmetry resembles the situation for non-extremal Kerr black holes [36, 37].”
The large D limit of General Relativity (2013, background): “Then the amplitudes and absorption probabilities above, although similar to the ones in [47], differ from them.”
DE SITTER MUSINGS (2012, background): “Though not an isometry of de Sitter space itself, this hidden SL(2,R), reminiscent of similar hidden symmetries found upon studying the wave-equation in a Kerr background [80], is related to particular conformal symmetries of dS4.”
Warped Conformal Field Theory (2012, background): “This fact has been partially understood for Kerr from a hidden conformal symmetry in the linearized equations of motion [64], but without some notion of a modular transformation, the entropy remains a puzzle.”