English

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

R2 v1 2026-06-21T18:32:04.056Z