Schr?dinger symmetry of Schwarzschild-(A)dS black hole mechanics

We show that the dynamics of Schwarzschild-(anti-)de Sitter [(A)dS] black holes admits a symmetry under the 2D Schrodinger 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 nontrivial potential controlled by the cosmological constant, and explicitly identifying the conserved charges for black hole mechanics. We expect the Schrodinger symmetry to drive the dynamics of quantum Schwarzschild-(A)dS black holes. This suggests that Schrodinger-preserving nonlinear deformations (of the Gross-Piteavskii type) should capture universal quantum gravity corrections to the black hole geometry. Such a scenario could be realized in condensed matter analog models.