REVIEW 9 cited by
Gravitational instantons and harmonic maps
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Gravitational instantons and harmonic maps
read the original abstract
We study the interaction between toric Ricci-flat metrics in dimension 4 and axisymmetric harmonic maps from the 3-dimensional Euclidean space into the hyperbolic plane. Applications include (1). The construction of complete Ricci-flat 4-manifolds that are non-spin, simply-connected, and with arbitrary second Betti number. Our method is non-perturbative and is based on ruling out conical singularities arising from axisymmetric harmonic maps. These metrics also give systematic counterexamples to various versions of the Riemannian black hole uniqueness conjecture. (2). A PDE classification result for axisymmetric harmonic maps of degree at most 1, via the Gibbons-Hawking ansatz and the LeBrun-Tod ansatz, in terms of axisymmetric harmonic functions. This is motivated by the study of hyperkahler and conformally Kahler gravitational instantons.
Forward citations
Cited by 9 Pith papers
-
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.
-
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.
-
A Comparison Theorem For the Mass of ALE and ALF Toric 4-Manifolds
The mass of toric ALE or ALF 4-manifolds with nonnegative scalar curvature is at least the mass of the corresponding toric gravitational instanton plus a term from its conical defects, with equality only when the mani...
-
A Comparison Theorem For the Mass of ALE and ALF Toric 4-Manifolds
The mass of any toric ALE/ALF 4-manifold with nonnegative scalar curvature is at least the mass of its corresponding toric gravitational instanton, corrected by conical angle defects, and equality holds only for the i...
-
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...
-
On Chen-Teo geometries with cosmological constant
Einstein metrics extending Chen-Teo geometries with cosmological constant are either Plebański-Demiański or anti-self-dual Weyl cases, yielding for lambda<0 a conformal infinity between asymptotically hyperbolic ends,...
-
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.
-
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-...
-
Geometry of gravitational instantons
A survey of classification results for hyperkähler and Hermitian gravitational instantons, constructions of non-Hermitian ones via harmonic maps, and open questions in the field.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.