Time-dependent multi-centre solutions from new metrics with holonomy Sim( n − 2)

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 holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a nonzero 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 generalized Laplace and Poisson equations on an ( n − 2)-dimensional Einstein base manifold. Explicit examples may be constructed in terms of generalized 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.