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Schrödinger symmetry in spherically-symmetric static minisuperspaces with matter fields

Taishi Sano1,* and Yuki Yokokura2,3,4,†

  • *Contact author: t.sano@ruri.waseda.jp
  • †Contact author: yokokura.yuki@kochi-tech.ac.jp
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Phys. Rev. D 114, 024055 – Published 21 July, 2026

DOI: https://doi.org/10.1103/x4sh-5sd9

Abstract

Schrödinger symmetry has been shown to emerge in a “fluid limit” from the full superspace to several minisuperspace models. To investigate one aspect of the robustness of this emergent symmetry, we consider two spherically-symmetric static minisuperspace 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), three-dimensional Schrödinger symmetry emerges, and the solution is the (anti–)de Sitter Reissner-Nordström spacetime; for model (ii), (2+n)D Schrödinger 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 two-dimensional Schrödinger symmetry holds with different lapse functions and minisuperspace 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 noncommuting with H generate a new theory with the Schrödinger symmetry and the transformed configuration is a solution to the new theory. These results reinforce the robustness of the emergent Schrödinger symmetry and open new frontiers for exploring dynamics of matter and gravity.

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Information

Phys. Rev. D 114, 024055– Published 21 July, 2026
  • Received 14 January 2026
  • Accepted 10 June 2026
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