Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications

Using a Hamiltonian treatment, charged thin shells, static and dynamic, in spherically symmetric spacetimes, containing black holes or other specific types of solutions, in d dimensional Lovelock-Maxwell theory are studied. The free coefficients that appear in the Lovelock theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. Using an Arnowitt-Deser-Misner (ADM) description, one then finds the Hamiltonian for the charged shell system. Variation of the Hamiltonian with respect to the canonical coordinates and conjugate momenta, and the relevant Lagrange multipliers, yields the dynamic and constraint equations. The vacuum solutions of these equations yield a division of the theory into two branches, namely d-2k-1>0 (which includes general relativity, Born-Infeld type theories, and other generic gravities) and d-2k-1=0 (which includes Chern-Simons type theories), where k is the parameter giving the highest power of the curvature in the Lagrangian. There appears an additional parameter {chi}=(-1){sup k+1}, which gives the character of the vacuum solutions. For {chi}=1 the solutions, being of the type found in general relativity, have a black hole character. For {chi}=-1 the solutions, being of a new type not found in general relativity, have a totally naked singularity character. Since there is a negative cosmologicalmore » constant, the spacetimes are asymptotically anti-de Sitter (AdS), and AdS when empty (for zero cosmological constant the spacetimes are asymptotically flat). The integration from the interior to the exterior vacuum regions through the thin shell takes care of a smooth junction, showing the power of the method. The subsequent analysis is divided into two cases: static charged thin shell configurations, and gravitationally collapsing charged dust shells (expanding shells are the time reversal of the collapsing shells). In the collapsing case, into an initially nonsingular spacetime with generic character or an empty interior, it is proved that the cosmic censorship is definitely upheld. Physical implications of the dynamics of such shells in a large extra dimension world scenario are also drawn. One concludes that, if such a large extra dimension scenario is correct, one can extract enough information from the outcome of those collisions as to know, not only the actual dimension of spacetime, but also which particular Lovelock gravity, general relativity or any other, is the correct one at these scales, in brief, to know d and k.« less