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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• Canonical quantum gravity
• Classical black holes
• General relativity equations & solutions
• General relativity formalism