Using a Hamiltonian treatment , charged thin shells , static and dynamic , in spherically symmetric spacetimes , containing black holes or other specific type 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 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 - 2 k - 1 > 0 ( which includes general relativity , Born-Infeld type theories , and other generic gravities ) and d - 2 k - 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 ) ^ { 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 cosmological constant , the spacetimes are asymptotically anti-de Sitter ( AdS ) , and AdS when empty .
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 non singular 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 .