There are no R3 x S1 Gravitational Instantons

Hugh Shanahan, Niall O'Murachadha

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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.
Original languageEnglish
Pages (from-to)1576
Number of pages2
JournalPhysical Review Letters
Issue number11
Publication statusPublished - Mar 1993

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