Hawking radiation from a collapsing dust sphere and its back reaction at the event horizon -Weak value approach-

TL;DR

This paper investigates the back reaction of Hawking radiation during dust sphere collapse by calculating the weak value of the energy-momentum tensor, revealing divergences at the horizon that challenge the semi-classical approximation.

Contribution

It introduces a weak value approach to analyze back reaction effects in a dynamical collapsing spacetime, highlighting limitations of the semi-classical approximation at the horizon.

Findings

Weak value diverges at the event horizon in the future.

Semi-classical Einstein equations break down at the horizon.

Future spacetime geometry differs from Schwarzschild due to back reaction.

Abstract

To see the back reaction of the Hawking radiation in a dynamical spacetime of the spherical gravitational collapse, we explicitly calculate the weak value of the energy-momentum tensor of the massless scalar field. The background geometry of a collapsing dust sphere is specified by 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 event horizon. The result is that in the remote future the weak value diverges at the event horizon. We argue that since the semi-classical approximation of the Einstein equation in the sense of the weak value breaks down there, the future geometry of the spacetime cannot be the Schwarzschild geometry.