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Cavities in curved spacetimes: The response of particle detectors

Aida Ahmadzadegan1,*, Eduardo Martín-Martínez2,3,4,†, and Robert B. Mann1,‡

  • 1Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 2Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 3Department of Applied Math, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 4Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo, Ontario N2L 2Y5, Canada

  • *aida.ahmad@uwaterloo.ca
  • †emartinm@uwaterloo.ca
  • ‡rbmann@uwaterloo.ca
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Phys. Rev. D 89, 024013 – Published 13 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.024013

Abstract

We introduce a method to compute a particle detector transition probability in spacetime regions of general curved spacetimes provided that the curvature is not above a maximum threshold. In particular we use this method to compare the response of two detectors, one in a spherically symmetric gravitational field and the other one in Rindler spacetime to compare the Unruh and Hawking effects: we study the vacuum response of a detector freely falling through a stationary cavity in a Schwarzschild background as compared to the response of an equivalently accelerated detector traveling through an inertial cavity in the absence of curvature. We find that as we set the cavity at increasingly further radii from the black hole, the thermal radiation measured by the detector approaches the quantity recorded by the detector in Rindler background showing in which way and at what scales the equivalence principle is recovered in the Hawking-Unruh effect. i.e. when the Hawking effect in a Schwarzschild background becomes equivalent to the Unruh effect in Rindler spacetime.

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Phys. Rev. D 89, 024013– Published 13 January, 2014
  • Received 18 October 2013

© 2014 American Physical Society

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