Abstract
Graviational instantons, solutions to the Euclidean Einstein equations, with toplogy × 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 ×. 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