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Journal Article

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

##### Fulltext (public)

1108.3841

(Preprint), 238KB

CQG_29_9_095020.pdf

(Any fulltext), 311KB

##### Supplementary Material (public)

There is no public supplementary material available

##### 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.