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Conformal Symmetries of the Einstein-Hilbert Action on Horizons of Stationary and Axisymmetric Black Holes

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons39396

Mei,  Jianwei
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1108.3841
(Preprint), 238KB

CQG_29_9_095020.pdf
(Any fulltext), 311KB

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Citation

Mei, J. (2012). Conformal Symmetries of the Einstein-Hilbert Action on Horizons of Stationary and Axisymmetric Black Holes. Classical and quantum gravity, 29(9): 095020. doi:10.1088/0264-9381/29/9/095020.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-4480-2
Abstract
We suggest a way to study possible conformal symmetries on black hole horizons. We do this by carrying out a Kaluza-Klein like reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the $m$-ignorable coordinates then becomes a global $SL(m,R)$ gauge symmetry of the reduced action. Related to each non-vanishing angular velocity there is a particular $SL(2,R)$ subgroup, which can be extended to the Witt algebra on the black hole horizons. The classical Einstein-Hilbert action thus has $k$-copies of infinite dimensional conformal symmetries on a given black hole horizon, with $k$ being the number of non-vanishing angular velocities of the black hole.