The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant

We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored.The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity.We investigate several conceptual and technical details that might be of interest for full (3+1) gravity. We use the new canonical variables introduced by Ashtekar, which simplifies the analysis tremendously.