Spherically symmetric geometrodynamics in Jordan and Einstein frames

Abstract 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).