Hawking radiation as seen by an infalling observer

TL;DR

This paper examines Hawking radiation from the perspective of an infalling observer during gravitational collapse, revealing how the perceived temperature varies with different spacetime foliations and approaches divergence at the horizon.

Contribution

It introduces a time-dependent analysis of Hawking radiation using the functional Schrödinger formalism, providing new insights into the observer-dependent temperature near black hole horizons.

Findings

In Schwarzschild frame, the temperature becomes thermal after crossing the horizon.

In Eddington-Finkelstein frame, the temperature remains finite at the horizon.

The local temperature diverges at the horizon in Schwarzschild coordinates.

Abstract

We investigate an important question of Hawking-like radiation as seen by an infalling observer during gravitational collapse. Using the functional Schrodinger formalism we are able to probe the time dependent regime which is out of the reach of the standard approximations like the Bogolyubov method. We calculate the occupation number of particles whose frequencies are measured in the proper time of an infalling observer in two crucially different space-time foliations: Schwarzschild and Eddington-Finkelstein. We demonstrate that the distribution in Schwarzschild reference frame is not quite thermal, though it becomes thermal once the horizon is crossed. We approximately fit the temperature and find that the local temperature increases as the horizon is approached, and diverges exactly at the horizon. In Eddington-Finkelstein reference frame the temperature at the horizon is finite, since the observer in that frame is not accelerated. These results are in agreement with what is generically expected in the absence of backreaction. We also discuss some subtleties related to the physical interpretation of the infinite local temperature in Schwarzschild reference frame.