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New asymptotically flat gravitational instanton

Department of Physics, National University of Singapore, Singapore 117551, Singapore

Phys. Rev. D 114, L021506 – Published 31 July, 2026

DOI: https://doi.org/10.1103/25dz-8t92

Abstract

A new two-parameter asymptotically flat (AF) toric gravitational instanton is identified as a special case of the Euclidean double Kerr-Newman-Unti-Tamburino solution, by imposing certain symmetry and regularity conditions on its rod structure. These conditions are solved explicitly, except for one which takes the form of a fifth-order polynomial equation. This gravitational instanton has Euler number $χ = 4$ and Hirzebruch signature $τ = 0$ , and its global topology is $C P^{2} # \bar{C P^{2}}$ with a circle $S^{1}$ removed appropriately. It is the third of an infinite sequence of AF toric gravitational instantons that was proved to exist by Li and Sun, the first two being the Kerr and Chen-Teo instantons. It is also the first known example of an AF gravitational instanton that is not Hermitian.

Physics Subject Headings (PhySH)

General relativity equations & solutions

Article Text

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New asymptotically flat gravitational instanton

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