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Gravitational instantons with S¹ symmetry
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Gravitational instantons with S¹ symmetry
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Uniqueness results for asymptotically locally flat and asymptotically flat $S^1$-symmetric gravitational instantons are proved using a divergence identity of the type used in uniqueness proofs for static black holes, combined with results derived from the $G$-signature theorem. Our results include a proof of the $S^1$-symmetric version of the Euclidean Black Hole Uniqueness conjecture, a uniqueness result for the Taub-bolt family of instantons, as well as a proof that an ALF $S^1$-symmetric instanton with the topology of the Chen-Teo family of instantons is Hermitian.
Forward citations
Cited by 5 Pith papers
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On the existence of toric ALE and ALF gravitational instantons
Existence and uniqueness of toric ALE and ALF Ricci-flat gravitational instantons for admissible rod structures, with toric self-dual instantons being multi-Eguchi-Hanson or multi-Taub-NUT.
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On toric self-dual Einstein gravitational instantons
Toric self-dual Einstein instantons with negative cosmological constant satisfying a global conformal Kähler extension condition are precisely the Calderbank-Pedersen-Singer multipole solutions.
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Mass Lower Bounds for Asymptotically Locally Flat Manifolds
For ALF 4-manifolds with an almost free circle symmetry and nonnegative scalar curvature, mass is nonnegative and at least (ℓ/16) times the degree of the asymptotic circle bundle; in the AF case, homology-trivial coor...
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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-...
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New asymptotically flat gravitational instanton
An explicit two-parameter metric is constructed for a new asymptotically flat toric gravitational instanton, the n=3 member of the Li-Sun family, with topology CP^2#CP^2 minus S^1.
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