Pre-Hawking radiation cannot prevent the formation of apparent horizon

TL;DR

This paper argues that pre-Hawking radiation cannot prevent the formation of apparent horizons during gravitational collapse, thus not resolving the black hole information paradox within semi-classical gravity.

Contribution

It demonstrates that pre-Hawking radiation is insufficient to stop apparent horizon formation, challenging recent proposals for solving the information paradox.

Findings

Pre-Hawking radiation's stress energy tensor is too small to affect collapse.

The collapsing shell always crosses the apparent horizon in finite proper time.

Energy radiated before horizon formation is limited to less than half of initial energy.

Abstract

As an attempt to solve the black hole information loss paradox, recently there has been the suggestion that, due to semi-classical effects, a pre-Hawking radiation must exist during the gravitational collapse of matter, which in turn prevents the apparent horizon from forming. Assuming the pre-Hawking radiation does exist, here we argue the opposite. First we note that the stress energy tensor near the horizon for the pre-Hawking radiation is far too small to do anything to the motion of a collapsing shell. Thus the shell will always cross the apparent horizon within a finite proper time. Moreovall, the amount of energy that can be radiated must be less than half of the total initial energy (if the particle starts at rest at infinity) before the shell becomes a null shell and cannot radiate any more without becoming tachyonic. We conclude that for any gravitational collapsing process within Einstein gravity and semi-classical quantum field theory, the formation of the apparent horizon is inevitable. Pre-Hawking radiation is therefore not a valid solution to the information paradox.