  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.
