Schrödinger symmetry of Schwarzschild-(A)dS black hole mechanics

Abstract

We show that the dynamics of Schwarzschild-(A)dS black holes admits a symmetry under the 2d Schrödinger group, whatever the sign or value of the cosmological constant. This is achieved by reformulating the spherically-symmetric reduction of general relativity as a 2d mechanical system with a non-trivial potential controlled by the cosmological constant, and explicitly identifying the conserved charges for black hole mechanics. We expect the Schrödinger symmetry to drive the dynamics of quantum Schwarzschild-(A)dS black holes. This suggests that Schrödinger-preserving non-linear deformations (of the Gross-Piteavskii type) should capture universal quantum gravity corrections to the black hole geometry. Such scenario could be realized in condensed matter analogue models.

arXiv comment10 pages, extended discussion and added references, version accepted by Phys.Rev.D