Isolated horizons: The classical phase space
The authors introduce the notion of a non-rotating isolated horizon, construct an action which yields Einstein's equations for histories admitting these horizons, and obtain a Hamiltonian framework in terms of real su(2)-valued fields. The boundary conditions that define isolated, non-rotating horizons \(\Delta\) are specified and those consequences of these boundary conditions that are needed in the Hamiltonian formulation and quantization are discussed. It is found that there is a surprising and interesting interplay between the space-time boundary conditions satisfied by \(\Delta\) and the Chern-Simons theory for a U(1) connection on \(\Delta\). The paper also contains a discussion of the resulting phase space, symplectic structure, constraints and gauge on which quantization is based. The boundary conditions, action and the Hamiltonian formulation for Maxwell and dilaton fields are considered in detail. The modifications that are necessary for incorporating electro-magnetic and dilatonic hair are discussed, too.
boundary conditions for non-rotating isolated horizons
scientific article; zbMATH DE number 1585176