We deal with a quantum, massless, scalar field, minimally coupled to the Schwarzschild-De Sitter metric. In this system we study the thermal radiation by a collapsing shell. In both two and four dimensions, Hawking radiation is found. In this system but without the shell and therefore with the past event horizon, the quantized energymomentum tensor is constructed with respect to the inequivalent vacuum states. The fluxes and energy distributions are studied and they are given the physical meaning. The results are consistent with other models for this problem.
We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in thermal equilibrium with a heat bath at the Hawking temperature, so the quantum field is in a state analogous to the Hartle-Hawking vacuum on an eternal black hole space-time.
We construct stationary black holes in SU(2) Einstein-Yang-Mills theory, which carry angular momentum and electric charge. Possessing non-trivial nonabelian magnetic fields outside their regular event horizon, they represent nonperturbative rotating hairy black holes.