Isolated horizons: Hamiltonian evolution and the first law - art. no. 104025

A framework was recently introduced to generalize black hole mechanics by r eplacing stationary event horizons with isolated horizons. That framework i s significantly extended. The extension is nontrivial in that not only do t he boundary conditions now allow the horizon to be distorted and rotating, but also the subsequent analysis is based on several new ingredients. Speci fically, although the overall strategy is closely related to that in the pr evious work, the dynamical variables, the action principle and the Hamilton ian framework are all quite different. More importantly, in the nonrotating case, the first law is shown to arise as a necessary nod sufficient condit ion for the existence of a consistent Hamiltonian evolution. Somewhat surpr isingly, this consistency condition in turn leads to new predictions even f or static black holes. To complement the previous work, the entire discussi on is presented in terms of tetrads and associated (real) Lorentz connectio ns.