Hawking Radiation from Black Holes Formed During Quantum Tunneling

We study the behaviour of scalar fields on background geometries which undergo quantum tunneling. The two examples considered are a moving mirror in flat space which tunnels through a potential barrier, and a false vacuum bubble which tunnels to form a black hole. WKB approximations to the Schrödinger and Wheeler-DeWitt equations are made, leading one to solve field equations on the Euclidean metric solution interpolating between the classically allowed geometries. The state of the field after tunneling can then be determined using the method of non-unitary Bogolubov transformations developed by Rubakov. It is shown that the effect of the tunneling is to damp any excitations initially present, and, in the case of the black hole, that the behaviour of fields on the Euclidean Kruskal manifold ensures that the late time radiation will be thermal at the Hawking temperature.