HIGHER-DIMENSIONAL CHARGED BLACK HOLES AS CONSTRAINED SYSTEMS

We construct a Lagrangian and Hamiltonian formulation for charged black holes in a d-dimensional maximally symmetric spherical space. By considering first new variables that give raise to an interesting dimensional reduction of the problem, we show that the introduction of a charge term is compatible with classical solutions to Einstein equations. In fact, we derive the well-known solutions for charged black holes, specially in the case of d = 4, where the Reissner-Nordstrom solution holds, without reference to Einstein field equations. We argue that our procedure may be of help for clarifying symmetries, dynamics and some quantum aspects of black holes.