A new AF gravitational instanton

TL;DR

This paper constructs a new asymptotically flat gravitational instanton with U(1)xU(1) symmetry, disproving the long-standing conjecture that only Schwarzschild and Kerr instantons are non-trivial AF instantons.

Contribution

It introduces a novel two-parameter AF gravitational instanton with specific topological and symmetry properties, constructed via the inverse-scattering method.

Findings

Disproves the conjecture about the uniqueness of Schwarzschild and Kerr instantons.

Provides explicit construction and properties of the new instanton.

Shows the instanton has topology CP^2 with a circle removed.

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.