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By analogy with Yang-Mills' theory, gravitational instantons are defined to be solutions of the classical Einstein equations which are non-singular on some section of complexified spacetime and in which the curvature dies away at large distances. The Schwarzschild and Taub-NUT solutions are simple examples, the latter being self-dual. A many Taub-NUT solution is also given. The significance of the two integrals in the curvature which are pure divergences is discussed.
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