Holonomy of Einstein Lorentzian manifolds

Abstract

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp., vacuum Einstein) Lorentzian manifold, the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.

Dedicated to to Mark Volfovich Losik on his 75th birthday. This version is an extended part of the previous version; another part of the previous version is extended and submitted as arXiv:1001.4441

References in corpus (5)

• Kundt Spacetimes
• Metrics With Vanishing Quantum Corrections
• Metrics that realize all Lorentzian holonomy algebras
• Supersymmetry, holonomy and Kundt spacetimes
• Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)

Cited by in corpus (5)

• On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
• On the Weyl Tensor Classification in All Dimensions and its Relation with Integrability Properties
• Examples of Einstein spacetimes with recurrent null vector fields
• Holonomy algebras of Einstein pseudo-Riemannian manifolds
• Decomposable $(5,6)$-solutions in eleven-dimensional supergravity