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 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. DAMTP-2007-88 MIFP-07-24