https://doi.org/10.1140/epjc/s10052-025-14447-9
Regular Article - Theoretical Physics
Spherically symmetric geometrodynamics in Jordan and Einstein frames
1
Specola Vaticana (Vatican Observatory), 00120, Vatican City, Vatican City State
2
INAF/OAS Bologna, via Gobetti 101, 40129, Bologna, Italy
3
INFN, Sezione di Bologna, via Irnerio 46, 40126, Bologna, Italy
4
Vatican Observatory Research Group, Steward Observatory, The University of Arizona, 933 North Cherry Avenue, 85721, Tucson, AZ, USA
5
INFN, Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044, Frascati, Italy
Received:
21
March
2025
Accepted:
17
June
2025
Published online:
4
July
2025
Spherically symmetric geometrodynamics is studied for scalar–tensor theory and Einstein General Relativity minimally coupled to a scalar field. We discussed the importance of boundary terms for non-compact space-like foliations and derived the equations of motion in the Hamiltonian formalism both in the Jordan and Einstein frames. On the reduced phase space obtained by gauge-fixing the lapse and the radial shift functions, the two frames are connected through a Hamiltonian canonical transformation. We discussed the effects of the singularity of the Hamiltonian canonical transformation connecting Jordan and Einstein frames for two static solutions (Fisher, Janis, Newman and Winicour solution in the Einstein frame and Bocharova–Bronnikov–Melnikov–Bekenstein black hole solution in the Jordan frame).
© The Author(s) 2025
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