1205.0118 (Yuki Kanai et al.)

Hawking radiation from a collapsing dust sphere and its back reaction at
the event horizon    [PDF]

Yuki Kanai, Akio Hosoya

We demonstrate the Hawking radiation in a dynamical spacetime of the spherical gravitational collapse and then evaluate its back reaction near the event horizon of the emerging Schwarzschild black hole. The background geometry of a collapsing dust sphere is specified, using the Painleve-Gullstrand coordinates in which the time coordinate coincides with the proper time of a free-falling observer and the metric tensor is regular at the horizon. To see the back reaction of the Hawking radiation, we explicitly calculate the weak value of the energy-momentum tensor of the massless scalar field. The result is that in the remote future the weak value diverges at the event horizon. We argue that since the Einstein equation in the semiclassical approximation breaks down there, the future geometry of the spacetime cannot be the Schwarzschild geometry.

View original: http://arxiv.org/abs/1205.0118