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

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.

A demonstration of the first law of black hole thermodynamics is added to section 3; and the introduction section is thoroughly revised; 22 pages

References in corpus (3)

• Cargese Lectures on the Kerr/CFT Correspondence
• Another Realization of Kerr/CFT Correspondence
• Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities

Cited by in corpus (4)

• Extended Symmetries at Black Hole Horizons in Generic Dimensions
• What happens to Petrov classification on horizons of axisymmetric dirty black holes
• Emergent Symmetry on Black Hole Horizons
• Fluctuating Black Hole Horizons