Path integral over black hole fluctuations

James W. York, Jr. and Bjoern S. Schmekel
Phys. Rev. D 72, 024022 – Published 27 July 2005

Abstract

Evaluating a functional integral exactly over a subset of metrics that represent the quantum fluctuations of the horizon of a black hole, we obtain a Schrödinger equation in null coordinate time for the key component of the metric. The equation yields a current that preserves probability if we use the most natural choice of functional measure. This establishes the existence of blurred horizons and a thermal atmosphere. It has been argued previously that the existence of a thermal atmosphere is a direct concomitant of the thermal radiation of black holes when the temperature of the hole is greater than that of its larger environment, which we take as zero.

  • Received 13 May 2005

DOI:https://doi.org/10.1103/PhysRevD.72.024022

©2005 American Physical Society

Authors & Affiliations

James W. York, Jr.* and Bjoern S. Schmekel

  • Department of Physics, Cornell University, Ithaca, New York 14853, USA

  • *Electronic address: york@astro.cornell.edu
  • Electronic address: bss28@cornell.edu

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Issue

Vol. 72, Iss. 2 — 15 July 2005

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