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arXiv · 2512.13651

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

Taishi Sano·Yuki Yokokura
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Abstract

Schr\"{o}dinger symmetry has been shown to emerge in a ``fluid limit" from the full superspace to several mini-superspace models. To investigate one aspect of the robustness of this emergent symmetry, we consider two spherically-symmetric static mini-superspace models with matter fields at the classical level: (i) a Maxwell field with a cosmological constant and (ii) $n$ massless scalar fields. By developing a method based on canonical transformations, we demonstrate that for model (i), 3D Schr\"odinger symmetry emerges, and the solution is the (anti-)de Sitter Reissner-Nordstr\"om spacetime, and for model (ii), $(2+n)$D Schr\"odinger symmetry appears, and the solution is a generalized Janis-Newman-Winicour spacetime and its ``interior", a Kantowski-Sachs type closed universe. Furthermore, for the vacuum model, we find that 2D Schr\"odinger symmetry holds with different lapse functions and mini-superspace coordinates, suggesting the potential, yet unconfirmed, covariance of the symmetry. Finally, we propose a physical interpretation of the symmetry under the Hamiltonian constraint $H$: symmetry generators commuting with $H$ map a solution to another one, while those non-commuting with $H$ generate a new theory with the Schr\"odinger symmetry and the transformed configuration is a solution to the new theory. These results reinforce the robustness of the emergent Schr\"odinger symmetry and open new frontiers for exploring dynamics of matter and gravity.

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Taishi Sano, Yuki Yokokura. 2025-12-15. Schr\"odinger Symmetry in Spherically-symmetric Static Mini-superspaces with Matter Fields. https://arxiv.org/abs/2512.13651

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