Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)

Abstract

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by Ghanam and Thompson. Here we reduce the problem of finding the general $n$-dimensional Einstein metric of SIM(n-2) holonomy, with and without a cosmological constant, to solving a set linear generalised Laplace and Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit examples may be constructed in terms of generalised harmonic functions. A dimensional reduction of these multi-centre solutions gives new time-dependent Kaluza-Klein black holes and monopoles, including time-dependent black holes in a cosmological background whose spatial sections have non-vanishing curvature.

Typos corrected; 29 pages

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• Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions
• On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
• A spacetime not characterised by its invariants is of aligned type II
• Geometry of Killing spinors in neutral signature
• Cosmological solutions from fake N=2 EYM supergravity
• One component of the curvature tensor of a Lorentzian manifold
• Type II universal spacetimes
• Almost universal spacetimes in higher-order gravity theories
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Charged Black Holes in a Five-dimensional Kaluza-Klein Universe
• Holonomy of Einstein Lorentzian manifolds
• Examples of Einstein spacetimes with recurrent null vector fields
• Black holes in an expanding universe and supersymmetry
• On the de Rham-Wu decomposition for Riemannian and Lorentzian manifolds
• Lovelock vacua with a recurrent null vector field
• How to find the holonomy algebra of a Lorentzian manifold
• Conformally flat Lorentzian manifolds with special holonomy groups
• Einstein Weyl Structures and de Sitter Supergravity
• Decomposable $(5,6)$-solutions in eleven-dimensional supergravity