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Waiting for Unruh

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Christopher J. Fewster

Benito A.

Professor of Mathematical Physics


How long does a uniformly accelerated observer need to interact with a quantum field in order to record thermality in the Unruh temperature? We address this question for a pointlike Unruh–DeWitt detector, coupled linearly to a real Klein–Gordon field of mass and treated within first order perturbation theory, in the limit of large detector energy gap . We first show that when the interaction duration is fixed, thermality in the sense of detailed balance cannot hold as , and this property generalises from the Unruh effect to any Kubo–Martin–Schwinger state satisfying certain technical conditions. We then specialise to a massless field in four spacetime dimensions and show that detailed balance does hold when grows as a power-law in as , provided the switch-on and switch-off intervals are stretched proportionally to and the switching function has sufficiently strong Fourier decay. By contrast, if grows by stretching a plateau in which the interaction remains at constant strength but keeping the duration of the switch-on and switch-off intervals fixed, detailed balance at requires to grow faster than any polynomial in , under mild technical conditions. The results also hold for a static detector in a Minkowski heat bath. The results limit the utility of the large regime as a probe of thermality in time-dependent versions of the Hawking and Unruh effects, such as an observer falling into a radiating black hole. They may also have implications on the design of prospective experimental tests of the Unruh effect.


Fewster, C. J., Juárez-Aubry, B. A., & Louko, J. (2016). Waiting for Unruh. Classical and Quantum Gravity, 33(16), Article 165003.

Journal Article Type Article
Acceptance Date Jun 24, 2016
Online Publication Date Jul 18, 2016
Publication Date Aug 18, 2016
Deposit Date Jul 7, 2017
Publicly Available Date Jul 7, 2017
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Electronic ISSN 1361-6382
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 33
Issue 16
Article Number 165003
Keywords Unruh effect, Unruh–DeWitt detector, Approach to detailed balance
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Additional Information This is an author-created, un-copyedited version of an article accepted for publication in Classical and Quantum Gravity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at


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