Hawking and Unruh radiation perception by different observers: applications of the effective temperature function (in Spanish)

TL;DR

This paper investigates how different observers perceive Hawking and Unruh radiation using the effective temperature function and Unruh-DeWitt detectors, revealing that perception depends on observer motion and position, with implications for black hole physics.

Contribution

It introduces a general expression for the effective temperature function and applies it to various observer trajectories, providing new insights into radiation perception near black holes.

Findings

Free-falling observers detect radiation at the horizon due to Doppler blue-shift.

The effective temperature function clarifies contributions from emitted radiation and observer acceleration.

A new 'pulsating vacuum' state reduces issues like the information paradox.

Abstract

We study the perception of the radiation phenomena of Hawking radiation and Unruh effect by using two main tools: the Unruh-DeWitt detectors and the effective temperature function (ETF), this last tool based on Bogoliubov transformations. Using the Unruh-DeWitt detectors we find an adiabatic expansion of the detection properties along linear trajectories with slowly varying acceleration in Minkowski, which allows us to calculate the spectrum detected, finding the thermal spectrum as the zeroth order contribution. Using the ETF we study the perception of Hawking radiation by observers following radial trajectories outside a Schwarzschild black hole. One of the most important results is that, in general, free-falling observers crossing the event horizon do detect some radiation, even when the field is in the Unruh vacuum state, due to a Doppler blue-shift that diverges at the horizon. We give a general expression for the ETF, which has a clear interpretation in terms of well-known physical phenomena. We discuss which contribution to the perception comes from the radiation emitted by the black hole, and which contribution is due to the Unruh effect caused by the movement of the observer. We conclude that the Unruh effect is not only due to the observer's proper acceleration and cannot even be defined locally, but is due to the observer's acceleration with respect to the asymptotic region. We apply the ETF to the analysis of different physical situations, in particular to a possible buoyancy scenario near the horizon due to Hawking radiation pressure. Finally, we propose a non-stationary vacuum state, which we call pulsating vacuum, for the radiation field outside a stellar object hovering closely to form an event horizon. In this vacuum state, we get nearly Hawking radiation emitted by the object, while avoiding the known problems of the information paradox and the trans-planckian problem.