Schwarzschild-(A)dS 黑洞力学的 Schrödinger 对称性
Schrödinger symmetry of Schwarzschild-(A)dS black hole mechanics
AI总结：
证明 Schwarzschild-(A)dS 黑洞动力学具有 2d Schrödinger 群对称性，通过将其球对称约化为 2d 力学系统并识别守恒荷，预期该对称性可驱动量子黑洞动力学并捕捉普适量子引力修正。
摘要：
我们证明，无论宇宙常数的符号或数值如何，Schwarzschild-(A)dS 黑洞的动力学均具有 2d Schrödinger 群下的对称性。这是通过将广义相对论的球对称约化重新表述为由宇宙常数控制的非平凡势的 2d 力学系统，并明确识别出黑洞力学的守恒荷来实现的。我们预期 Schrödinger 对称性将驱动量子 Schwarzschild-(A)dS 黑洞的动力学。这表明保持 Schrödinger 不变的（Gross-Piteavskii 型）非线性形变应能捕捉黑洞几何的普适量子引力修正。该情景可在凝聚态类比模型中实现。
英文摘要：
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.
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