A new two-parameter AF toric gravitational instanton with Euler number 4 and Hirzebruch signature 0 is obtained as a special case of the Euclidean double Kerr-NUT solution, the third in a sequence after Kerr and Chen-Teo, and the first known non-Hermitian Ricci-flat example.
A new AF gravitational instanton
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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.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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New asymptotically flat gravitational instanton
A new two-parameter AF toric gravitational instanton with Euler number 4 and Hirzebruch signature 0 is obtained as a special case of the Euclidean double Kerr-NUT solution, the third in a sequence after Kerr and Chen-Teo, and the first known non-Hermitian Ricci-flat example.