Euclidean Schwarzschild negative mode

Bruce Allen
Phys. Rev. D 30, 1153 – Published 15 September 1984
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Abstract

The Euclidean (imaginary time) Schwarzschild solution of general relativity is known to possess a spin-2 metric perturbation which decreases its Euclidean action. This "negative mode" contributes an imaginary part to the effective action, and renders hot flat space unstable against the nucleation of black holes. In this paper, we enclose the black hole in a spherical "box" by imposing boundary conditions on the perturbations. Two conditions, which correspond to a fixed temperature (isothermal wall) and fixed energy (reflecting wall) are examined. The isothermal boundary condition eliminates the negative mode if the box is small enough, and stabilizes hot flat space.

  • Received 18 May 1984

DOI:https://doi.org/10.1103/PhysRevD.30.1153

©1984 American Physical Society

Authors & Affiliations

Bruce Allen

  • Department of Physics, University of California, Santa Barbara, California 93106

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Vol. 30, Iss. 6 — 15 September 1984

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