A new AF gravitational instanton
arXiv:1107.0763 · doi:10.1016/j.physletb.2011.07.076
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 Ï=3 and Hirzebruch signature Ï=1, and its global topology is CP^2 with a circle S^1 removed appropriately. Various other properties of this gravitational instanton are also discussed.
10 pages, 2 figures, LaTeX