Schr\"odinger symmetry of Schwarzschild-(A)dS black hole mechanics

TL;DR

This paper demonstrates that Schwarzschild-(A)dS black hole dynamics exhibit a Schr"odinger symmetry, which could influence quantum gravity corrections and be explored through condensed matter analogues.

Contribution

It reveals a Schr"odinger symmetry in the reduced 2d black hole mechanics, providing a new perspective on black hole dynamics and potential quantum gravity effects.

Findings

Identifies Schr"odinger symmetry in Schwarzschild-(A)dS black holes

Reformulates black hole mechanics as a 2d system with symmetry

Suggests universal quantum corrections via Schr"odinger-preserving deformations

Abstract

We show that the dynamics of Schwarzschild-(A)dS black holes admits a symmetry under the 2d Schr\"odinger 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 Schr\"odinger symmetry to drive the dynamics of quantum Schwarzschild-(A)dS black holes. This suggests that Schr\"odinger-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.