There are no R3×S1 vacuum gravitational instantons

Niall Ó Murchadha and Hugh Shanahan
Phys. Rev. Lett. 70, 1576 – Published 15 March 1993
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Abstract

Graviational instantons, solutions to the Euclidean Einstein equations, with toplogy R3×S1 arise naturally in finite-temperature quantum gravity. It is shown here that all such instantons must have the same asymptotic structure as the Schwarzschild instanton. From this follows that if the Ricci tensor of such a manifold is non-negative it must be flat. Hence there is no nontrivial vacuum gravitational instanton on R3×S1. This places a significant restriction on the instabilities of hot flat space. Another consequence is that any static vacuum Lorentzian Kaluza-Klein solution is flat.

  • Received 20 August 1992

DOI:https://doi.org/10.1103/PhysRevLett.70.1576

©1993 American Physical Society

Authors & Affiliations

Niall Ó Murchadha and Hugh Shanahan

  • Department of Physics, University College, Cork, Ireland

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Issue

Vol. 70, Iss. 11 — 15 March 1993

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