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

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.

21 pages, 9 figures

References in corpus (10)

• The Unruh effect and its applications
• Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?
• Onset and decay of the 1+1 Hawking-Unruh effect: what the derivative-coupling detector saw
• A quantum peek inside the black hole event horizon
• Black hole kinematics: the "in"-vacuum energy density and flux for different observers
• A Little Excitement Across the Horizon
• More Excitement Across the Horizon
• The effective Tolman temperature in curved spacetimes
• Semiclassical solution of black hole information paradox
• Globally hyperbolic evaporating black hole and the information loss issue

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