Hamiltonian dynamics of Lovelock black holes with spherical symmetry

Understand

We consider spherically symmetric black holes in generic Lovelock gravity.

• Using geometrodynamical variables we do a complete Hamiltonian analysis, including derivation of the super-Hamiltonian and super-momentum constraints and verification of suitable boundary conditions for asymptotically flat black holes.
• Our analysis leads to a remarkably simple fully reduced Hamiltonian for the vacuum gravitational sector that provides the starting point for the quantization of Lovelock block holes.
• Finally, we derive the completely reduced equations of motion for the collapse of a spherically symmetric charged, self-gravitating complex scalar field in generalized flat slice (Painlev\'{e}-Gullstrand) coordinates.