There are no R(3) x S(1) vacuum gravitational instantons

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Date
1993
Authors
Ó Murchadha, Niall
Shanahan, Hugh
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American Physical Society
Published Version
10.1103/PhysRevLett.70.1576
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Abstract
Gravitational instantons, solutions to the Euclidean Einstein equations, with topology R3 x 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 x 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.
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Keywords
Graviational instantons , Schwarzschild instanton , Euclidean Einstein equations
Citation
Ó Murchadha, N. and Shanahan, H. (1993) 'There are no R(3) x S(1) vacuum gravitational instantons', Physical Review Letters, 70(11), 1576-1578 (3pp). doi: 10.1103/PhysRevLett.70.1576
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https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1576
URI
https://hdl.handle.net/10468/4666
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Physics - Journal Articles
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© 1993, American Physical Society