Radially falling test particle approaching an evaporating black hole

TL;DR

This paper models a non-rotating black hole's evaporation using a global time coordinate, analyzing how a test particle falls towards it and challenging previous assumptions about horizon crossing.

Contribution

It introduces a non-singular global time framework to study particle infall in an evaporating black hole, highlighting the importance of coordinate choice and revealing the horizon's position.

Findings

Particle can pass the Schwarzschild radius before black hole evaporates.

The true event horizon lies inside the Schwarzschild radius for a shrinking black hole.

A global time coordinate avoids singularities at the horizon.

Abstract

A simple model for an evaporating non-rotating black hole is considered, employing a global time that does not become singular at the putative horizon. The dynamics of a test particle falling radially towards the center of the black hole is then investigated. Contrary to a previous approach, we find that the particle may pass the Schwarzschild radius before the black hole has gone. Backreaction effects of Hawking radiation on the space-time metric are not considered, rather a purely kinematical point of view is taken here. The importance of choosing an appropriate time coordinate when describing physical processes in the vicinity of the Schwarzschild radius is emphasized. For a shrinking black hole, the true event horizon is found to be inside the sphere delimited by that radius.