About: Gravitational instanton

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In mathematical physics and differential geometry, a gravitational instanton is a four-dimensional complete Riemannian manifold satisfying the vacuum Einstein equations. They are so named because they are analogues in quantum theories of gravity of instantons in Yang–Mills theory. In accordance with this analogy with self-dual Yang–Mills instantons, gravitational instantons are usually assumed to look like four dimensional Euclidean space at large distances, and to have a self-dual Riemann tensor. Mathematically, this means that they are asymptotically locally Euclidean (or perhaps asymptotically locally flat) hyperkähler 4-manifolds, and in this sense, they are special examples of Einstein manifolds. From a physical point of view, a gravitational instanton is a non-singular solution of th

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rdf:type	yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553 yago:WikicatRiemannianManifolds
rdfs:label	Gravitational instanton (en) 重力インスタントン (ja)
rdfs:comment	重力インスタントン（じゅうりょく - ）とは、以下の3つの性質を持つ4次元リーマン多様体のことである。 1. * リッチ平坦 2. * （self-dual）なリーマン曲率テンソルをもつ 3. * 無限遠で局所的に平坦（asymptotically locally flat）である（しかし実は、2. ならば 1. が言える。）あるいは、もっと広い意味で、3. を満たしリッチ曲率が計量に比例している（いわゆる宇宙定数がある）ものを言う。ヤン・ミルズ理論のインスタントンとの類似から、そう呼ばれる。ALE（Asymptotically Locally Euclidean）空間とも呼ばれる。 (ja) In mathematical physics and differential geometry, a gravitational instanton is a four-dimensional complete Riemannian manifold satisfying the vacuum Einstein equations. They are so named because they are analogues in quantum theories of gravity of instantons in Yang–Mills theory. In accordance with this analogy with self-dual Yang–Mills instantons, gravitational instantons are usually assumed to look like four dimensional Euclidean space at large distances, and to have a self-dual Riemann tensor. Mathematically, this means that they are asymptotically locally Euclidean (or perhaps asymptotically locally flat) hyperkähler 4-manifolds, and in this sense, they are special examples of Einstein manifolds. From a physical point of view, a gravitational instanton is a non-singular solution of th (en)
dcterms:subject	4-manifolds Quantum gravity Riemannian manifolds Mathematical physics
Wikipage page ID	2618270 (xsd:integer)
Wikipage revision ID	1114231522 (xsd:integer)
Link from a Wikipage to another Wikipage	Schwarzschild metric De Sitter space Hyperkähler manifold Path integral formulation Characteristic class Instanton 4-manifolds Quantum gravity Cosmological constant SO(4) Yang–Mills theory Riemannian manifolds Einstein–Hilbert action N-sphere Coordinate system Calabi–Yau manifold String theory dbr:Complex_projective_plane Fubini–Study metric Gibbons–Hawking Ansatz Spin group Subgroup Mathematical physics Pontryagin class Cyclic group Euclidean space Euler angles Dirac spinor Gravitational anomaly Gravitational singularity Lens space Riemann curvature tensor Pseudo-Riemannian manifold Quantum gravity Riemannian manifold Cotangent bundle Hyperkähler quotient Mathematical physics Chern class K3 surface Kahler manifold Kerr metric Eguchi–Hanson space Einstein manifold Differential geometry Dihedral group Kähler manifold Orbifold Scale factor Twistor theory Vacuum Euler characteristic Gibbons–Hawking–York boundary term Taub–NUT space Weyl tensor Octahedral group Spin structure Friedmann Universe Riemann tensor Tetrahedral group Einstein equation Icosahedral group Three-sphere Complete metric dbr:Hirzebruch_signature dbr:Page_space dbr:Rarita—Schwinger_index dbr:Taub-bolt_metric
Link from a Wikipage to an external page	https://projecteuclid.org/euclid.cmp/1103905051 https://escholarship.org/uc/item/2qm8r91p https://escholarship.org/uc/item/5qx4k926
sameAs	Gravitational instanton Gravitational instanton Gravitational instanton Gravitational instanton Gravitational instanton
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