Euclidean Schwarzschild negative mode

Allen, Bruce

doi:10.1103/PhysRevD.30.1153

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Euclidean Schwarzschild negative mode

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Allen, Bruce
Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Citation

Allen, B. (1984). Euclidean Schwarzschild negative mode. Physical Review D, 30(6), 1153-1157. doi:10.1103/PhysRevD.30.1153.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5E30-1

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.