Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications

Abstract

Using a Hamiltonian treatment, charged thin shells in spherically symmetric spacetimes in d dimensional Lovelock-Maxwell theory are studied. The coefficients of the theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. After writing the action and the Lagrangian for a spacetime comprised of an interior and an exterior regions, with a thin shell as a boundary in between, one finds the Hamiltonian using an ADM description. For spherically symmetric spacetimes, one reduces the relevant constraints. The dynamic and constraint equations are obtained. The vacuum solutions yield a division of the theory into two branches, d-2k-1>0 (which includes general relativity, Born-Infeld type theories) and d-2k-1=0 (which includes Chern-Simons type theories), where k gives the highest power of the curvature in the Lagrangian. An additional parameter, chi, gives the character of the vacuum solutions. For chi=1 the solutions have a black hole character. For chi=-1 the solutions have a totally naked singularity character. The integration through the thin shell takes care of the smooth junction. The subsequent analysis is divided into two cases: static charged thin shell configurations, and gravitationally collapsing charged dust shells. Physical implications are drawn: if such a large extra dimension scenario is correct, one can extract enough information from the outcome of those collapses as to know, not only the actual dimension of spacetime, but also which particular Lovelock gravity, is the correct one.