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arXiv · 1108.3841

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

Jianwei Mei
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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.

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Jianwei Mei. 2012-02-19. Conformal Symmetries of the Einstein-Hilbert Action on Horizons of Stationary and Axisymmetric Black Holes. https://doi.org/10.1088/0264-9381%2F29%2F9%2F095020

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