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

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arxiv 2302.07644 v3 pith:YZNNE5TN submitted 2023-02-15 gr-qc

Jibril Ben Achour , Etera R. Livine , Daniele Oriti This is my paper · ORCID
classification gr-qc
keywords blackschrholeodingerschwarzschild-symmetryconstantcosmological
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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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Cited by 3 Pith papers

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  1. Love numbers of black p-branes: fine tuning, Love symmetries, and their geometrization

    hep-th 2025-02 accept novelty 8.0 of 10

    Scalar Love numbers of non-dilatonic black p-branes vanish for integer rescaled multipoles, extremal p-branes give exactly zero static Love numbers, and the hidden symmetries behind these vanishings become near-horizo...

  2. Schr\"odinger Symmetry in Spherically-symmetric Static Mini-superspaces with Matter Fields

    gr-qc 2025-12 conditional novelty 7.0 of 10

    Spherically symmetric static gravity with Maxwell or massless-scalar matter exhibits Schrödinger symmetry after a canonical transformation, yielding (A)dS-Reissner-Nordström and generalized Janis-Newman-Winicour solutions.

  3. Entanglement Entropy of Quantum Corners

    hep-th 2025-07 conditional novelty 6.0 of 10

    For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.

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