Reflection and Transmission at the Apparent Horizon during Gravitational Collapse

TL;DR

This paper analyzes quantum wave-functionals during gravitational collapse, revealing that apparent horizons act as partial reflectors with transmission related to Hawking radiation, potentially enabling information transfer from interior to exterior.

Contribution

It demonstrates that apparent horizons behave as partial reflectors with Hawking-temperature-dependent transmission, affecting the wave-functionals of collapsing dust shells in quantum gravity.

Findings

Ingoing dust modes outside the horizon are accompanied by suppressed outgoing modes inside.

The apparent horizon acts as a partial reflector with probability given by the Boltzmann factor.

Transmission of interior outgoing waves through the horizon may enable information transfer.

Abstract

We examine the wave-functionals describing the collapse of a self-gravitating dust ball in an exact quantization of the gravity-dust system. We show that ingoing (collapsing) dust shell modes outside the apparent horizon must necessarily be accompanied by outgoing modes inside the apparent horizon, whose amplitude is suppressed by the square root of the Boltzmann factor at the Hawking temperature. Likewise, ingoing modes in the interior must be accompanied by outgoing modes in the exterior, again with an amplitude suppressed by the same factor. A suitable superposition of the two solutions is necessary to conserve the dust probability flux across the apparent horizon, thus each region contains both ingoing and outgoing dust modes. If one restricts oneself to considering only the modes outside the apparent horizon then one should think of the apparent horizon as a partial reflector, the probability for a shell to reflect being given by the Boltzmann factor at the Hawking temperature determined by the mass contained within it. However, if one considers the entire wave function, the outgoing wave in the exterior is seen to be the transmission through the horizon of the interior outgoing wave that accompanies the collapsing shells. This transmission could allow information from the interior to be transferred to the exterior.