Hidden conformal symmetry of the Kerr black hole

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.024008· OSTI ID:21410118

Castro, Alejandra; Maloney, Alexander; Strominger, Andrew ^[1]

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1. Physics Department, McGill University, Montreal, Quebec (Canada)

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{sub L}=c{sub 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{ne}{radical}(J). Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The 2{pi} periodic identification of the azimuthal angle {phi} is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures T{sub L}=M{sup 2}/2{pi}J and T{sub R}={radical}(M{sup 4}-J{sup 2})/2{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{sub L}=c{sub R}=12J 2D CFT at temperatures (T{sub L},T{sub R}) for every value of M and J.

• OSTI ID: 21410118
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevD.82.024008; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BLACK HOLES
CONFORMAL INVARIANCE
KERR FIELD
MASS
PERIODICITY
QUANTUM FIELD THEORY
SCATTERING AMPLITUDES
SPACE-TIME
SPIN
TWO-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS
AMPLITUDES
ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
GRAVITATIONAL FIELDS
INVARIANCE PRINCIPLES
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
VARIATIONS