What Hawking Radiation Looks Like as You Fall into a Black Hole

TL;DR

This paper investigates how a freely falling detector perceives Hawking radiation near a black hole horizon, revealing that the detector's response is dominated by switching effects and proposing an operational temperature measure that varies smoothly across the horizon.

Contribution

It introduces an operational definition of effective temperature for infalling observers and demonstrates its smooth variation, aligning with higher-dimensional embedding predictions.

Findings

Detector response is dominated by switching effects.

Effective temperature increases smoothly from the Hawking temperature to twice that at the horizon.

Higher-dimensional embeddings match the measured effective temperature near the horizon.

Abstract

We study the measurements of a freely falling Unruh-DeWitt particle detector near the horizon of a semiclassical Schwarzschild black hole. Our results show that the detector's response increases smoothly as it approaches and crosses the horizon in both the Hartle-Hawking and Unruh vacua. However, these measurements are dominated by the effects of switching the detector on and off, rather than by the detection of Hawking radiation particles. We demonstrate that a freely falling Unruh-DeWitt detector cannot directly measure Hawking radiation near the horizon because the time required for thermalization is longer than the time spent near the horizon. We propose an operational definition of the effective temperature along an infalling trajectory based on measurements by a particle detector. Using this method, we find that the effective temperature measured by a freely falling observer in the Hartle-Hawking vacuum increases smoothly from the Hawking temperature far from the horizon to twice the Hawking temperature at the horizon, and continues to rise into the interior of the black hole. This effective temperature closely matches an analytical prediction derived by embedding Schwarzschild spacetime into a higher-dimensional Minkowski space, suggesting that further exploration of higher-dimensional embeddings could provide new insights into the near-horizon behavior of black holes.