A new AF gravitational instanton
General Relativity and Quantum Cosmology
2011-09-07 v1
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 \chi=3 and Hirzebruch signature \tau=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.
Keywords
Cite
@article{arxiv.1107.0763,
title = {A new AF gravitational instanton},
author = {Yu Chen and Edward Teo},
journal= {arXiv preprint arXiv:1107.0763},
year = {2011}
}
Comments
10 pages, 2 figures, LaTeX