Phys. Rev. Lett. 70, 1576–1578 (1993)There are no R3×S1 vacuum gravitational instantonsReceived 20 August 1992; published in the issue dated 15 March 1993 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. © 1993 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.70.1576
DOI:
10.1103/PhysRevLett.70.1576
PACS:
04.60.+n, 04.50.+h
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