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

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. ∗Email: [email protected]