Time-dependent multi-centre solutions from new metrics with holonomy SIM(n-2)
Sep, 200729 pages
Published in:
- Class.Quant.Grav. 25 (2008) 125015
e-Print:
- 0709.2440 [hep-th]
Report number:
- DAMTP-2007-88,
- MIFP-07-24
View in:
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Abstract: (arXiv)
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 -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.- field theory: vector
- space-time: Euclidean
- space-time: Minkowski
- Einstein equation: solution
- time dependence
- holonomy
- spinor
- Kaluza-Klein model
- black hole
- monopole
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