Hawking radiation and the boomerang behavior of massive modes near a horizon

G. Jannes, P. Maïssa, T. G. Philbin, and G. Rousseaux
Phys. Rev. D 83, 104028 – Published 17 May 2011

Abstract

We discuss the behavior of massive modes near a horizon based on a study of the dispersion relation and wave packet simulations of the Klein-Gordon equation. We point out an apparent paradox between two (in principle equivalent) pictures of black-hole evaporation through Hawking radiation. In the picture in which the evaporation is due to the emission of positive-energy modes, one immediately obtains a threshold for the emission of massive particles. In the picture in which the evaporation is due to the absorption of negative-energy modes, such a threshold apparently does not exist. We resolve this paradox by tracing the evolution of the positive-energy massive modes with an energy below the threshold. These are seen to be emitted and move away from the black-hole horizon, but they bounce back at a “red horizon” and are reabsorbed by the black hole, thus compensating exactly for the difference between the two pictures. For astrophysical black holes, the consequences are curious but do not affect the terrestrial constraints on observing Hawking radiation. For analogue-gravity systems with massive modes, however, the consequences are crucial and rather surprising.

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  • Received 4 February 2011

DOI:https://doi.org/10.1103/PhysRevD.83.104028

© 2011 American Physical Society

Authors & Affiliations

G. Jannes1,2, P. Maïssa1, T. G. Philbin3, and G. Rousseaux1,*

  • 1Université de Nice Sophia Antipolis, Laboratoire J.-A. Dieudonné, UMR CNRS-UNS 6621, Parc Valrose, 06108 Nice Cedex 02, France
  • 2Low Temperature Laboratory, Aalto University School of Science, PO Box 15100, 00076 Aalto, Finland
  • 3School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland, United Kingdom

  • *Germain.Rousseaux@unice.fr

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Vol. 83, Iss. 10 — 15 May 2011

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