Hamiltonian dynamics of Lovelock black holes with spherical symmetry

TL;DR

This paper performs a Hamiltonian analysis of spherically symmetric Lovelock black holes, deriving simplified equations and constraints that facilitate their quantization and study of collapse dynamics.

Contribution

It provides a complete Hamiltonian formulation for Lovelock black holes, including boundary conditions and reduced equations of motion for collapse scenarios.

Findings

Derived a simple, fully reduced Hamiltonian for vacuum Lovelock black holes.

Established boundary conditions for asymptotically flat solutions.

Presented equations of motion for charged scalar field collapse.

Abstract

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.