We present the Hamiltonian, quasilocal energy, and angular momentum for a spacetime region spatially bounded by two timelike surfaces. The results are applied to the particular case of a spacetime representing an eternal black hole. It is shown that in the case when the boundaries are located in two different wedges of the Kruskal diagram, the Hamiltonian is of the form , where and are the Hamiltonian functions for the right and left wedges, respectively. The obtained results strongly suggest a generalization beyond small perturbations of a thermofield dynamics description of quantum effects in black holes.