Abstract
We present novel methods to numerically address the problem of characterizing the response of particle detectors in curved spacetimes. These methods allow for the integration of the Wightman function, at least in principle, in rather general backgrounds. In particular we will use this tool to further understand the nature of conformal massless scalar Hawking radiation from a Schwarzschild black hole in anti-de Sitter space. We do that by studying an Unruh-DeWitt detector at rest above the horizon and in circular geodesic orbit. The method allows us to see that the response rate shows peaks at certain characteristic frequencies, which correspond to the quasinormal modes (QNMs) of the space-time. It is in principle possible to apply these techniques to more complicated and interesting physical scenarios, e.g. geodesic infall or multiple detector entanglement evolution, or the study of the behaviour of quantum correlations in spacetimes with black hole horizons.
Highlights
In recent years, there has been renewed interest in verifying the existence of Hawking radiation in spacetimes with black hole event horizons using the Unruh-DeWitt detector formalism
A recent proposal [1] has allowed for an insightful study of the thermal response of static and circular-geodesic particle detectors in Schwarzschild backgrounds, and there are new and promising results in progress regarding a detector model that is free from infrared divergences [2], which may be helpful in studying the response of particle detectors across event horizons
The Hawking effect was first discovered in Schwarzschild spacetime in 1974 [3]
Summary
There has been renewed interest in verifying the existence of Hawking radiation in spacetimes with black hole event horizons using the Unruh-DeWitt detector formalism. Unruh [4] suggested the idea of a model particle detector, in order to operationalize the idea of “observing” the radiated particles This method was recently applied in [1] to a study of the Schwarzschild spacetime. We will analyze the radiation emitted by a black hole in a 4-dimensional asymptotically anti-de Sitter space by means of the vacuum response of a particle detector in this background. This form holds whether the detector is a two-level system or a harmonic oscillator; the differences only become apparent at higher order in perturbation theory and do not yield a qualitative difference as compared with the twolevel quantum emitter [15] For this reason, abusing notation, the response function itself is often called the ‘probability’ [14]. We explore some possible interpretations of the numerical results
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