Per Kraus

We consider the modification of the formulas for black hole radiation, due to the self-gravitation of the radiation. This is done by truncating the coupled particle-hole system to a small set of modes, that are plausibly the most significant ones, and quantizing the reduced system. In this way we find that the particles no longer move along geodesics, nor is the action along the rays zero for a massless particle. The radiation is no longer thermal, but is corrected in a definite way that we calculate. Our methods can be extended in a straightforward manner to discuss correlations in the radiation, or between incoming particles and the radiation.

Guided by a Hamiltonian treatment of spherically symmetric geometry, we find a remarkably simple -- stationary, but not static -- form for the line element of Schwarzschild (and Reissner-Nordstrom) geometry. The line element continues smoothly through the horizon; by exploiting this feature we are able to give a very simple and physically transparent derivation of the Hawking radiance. We construct the complete Penrose diagram by enforcing time-reversal symmetry. Finally we outline how an improved treatment of the radiance, including effects of self-gravitation, can be obtained.

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 Schrodinger 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.