Einstein Manifolds, Abelian Instantons, Bundle Reduction, and the Cosmological Constant

Details Einstein Manifolds, Abelian Instantons, Bundle Reduction, and the Cosmological Constant Einstein Manifolds, Abelian Instantons, Bundle Reduction, and the Cosmological Constant

2000-09-04

arxiv.org/abs/gr-qc/0009007v1

Class.Quant.Grav. 18 (2001) 709-718

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, RevTex file

Scientific paper

10.1088/0264-9381/18/4/310

The anti-self-dual projection of the spin connections of certain four-dimensional Einstein manifolds can be Abelian in nature. These configurations signify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated on the existence of a covariantly constant field. It turns out that even without fundamental Higgs fields and other physical matter, gravitational self-interactions can generate this mechanism if the cosmological constant is non-vanishing. This article identifies the order parameter, and clarifies how these Abelian instanton solutions are associated with a Higgs triplet which causes the bundle reduction from SO(3) gauge group to U(1).

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