Hawking radiation as perceived by different observers

TL;DR

This paper investigates how different observers perceive Hawking radiation near a Schwarzschild black hole using a novel time-dependent effective temperature method, revealing observer-dependent perceptions and effects at the horizon.

Contribution

It introduces a non-stationary vacuum state and a method to analyze Hawking radiation perception by various observers, highlighting the observer-dependent nature of the radiation.

Findings

Freely-falling observers do not see vacuum at the horizon.

Perceived temperature by free-fall observers increases near the horizon.

Doppler effect causes divergence in perceived temperature at horizon crossing.

Abstract

We use a method recently introduced in Barcel\'o et al (2011 Phys. Rev. D 83 41501), to analyse Hawking radiation in a Schwarzschild black hole as perceived by different observers in the system. The method is based on the introduction of an 'effective temperature' function that varies with time. First we introduce a non-stationary vacuum state for a quantum scalar field, which interpolates between the Boulware vacuum state at early times and the Unruh vacuum state at late times. In this way we mimic the process of switching on Hawking radiation in realistic collapse scenarios. Then, we analyse this vacuum state from the perspective of static observers at different radial positions, observers undergoing a free-fall trajectory from infinity and observers standing at rest at a radial distance and then released to fall freely towards the horizon. The physical image that emerges from these analyses is rather rich and compelling. Among many other results, we find that generic freely-falling observers do not perceive vacuum when crossing the horizon, but an effective temperature a few times larger than the one that they perceived when it started to free-fall. We explain this phenomenon as due to a diverging Doppler effect at horizon crossing.