A new AF gravitational instanton
Abstract
It has long been conjectured that the Euclidean Schwarzschild and Euclidean Kerr instantons are the only non-trivial asymptotically flat (AF) gravitational instantons. In this letter, we show that this conjecture is false by explicitly constructing a new two-parameter AF gravitational instanton with a U(1)xU(1) isometry group, using the inverse-scattering method. It has Euler number =3 and Hirzebruch signature τ=1, and its global topology is CP2 with a circle S1 removed appropriately. Various other properties of this gravitational instanton are also discussed.
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