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arXiv · 2302.07644

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

Jibril Ben Achour·Etera R. Livine·Daniele Oriti
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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.

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Jibril Ben Achour, Etera R. Livine, Daniele Oriti. 2023-02-15. Schr\"odinger symmetry of Schwarzschild-(A)dS black hole mechanics. https://arxiv.org/abs/2302.07644

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