The Jordan and Einstein frames are connected by a Hamiltonian canonical transformation only after gauge-fixing lapse and shift, and this maps the FJNW naked singularity to the BBMB black hole.
Spherically Symmetric Geometrodynamics in Jordan and Einstein frames
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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 and derived the equations of motion in the Hamiltonian canonical formalism both in the Jordan and Einstein frames. These two frames are connected through an Hamiltonian canonical transformation on the reduced phase space obtained gauge-fixing the lapse and the radial shift functions. 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).
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Aspects of Geometrodynamics in the Jordan and Einstein Frames
The Jordan and Einstein frames are connected by a Hamiltonian canonical transformation only after gauge-fixing lapse and shift, and this maps the FJNW naked singularity to the BBMB black hole.