Ricci Nilsoliton Black Holes

Details Ricci Nilsoliton Black Holes Ricci Nilsoliton Black Holes

2007-07-18

arxiv.org/abs/0707.2755v2

J.Geom.Phys.58:1253-1264,2008

Physics

High Energy Physics

High Energy Physics - Theory

19 pages; to appear in JGP

Scientific paper

10.1016/j.geomphys.2008.05.001

We follow a constructive approach and find higher-dimensional black holes with Ricci nilsoliton horizons. The spacetimes are solutions to Einstein's equation with a negative cosmological constant and generalises therefore, anti-de Sitter black hole spacetimes. The approach combines a work by Lauret -- which relate so-called Ricci nilsolitons and Einstein solvmanifolds -- and an earlier work by the author. The resulting black hole spacetimes are asymptotically Einstein solvmanifolds and thus, are examples of solutions which are not asymptotically Anti-de Sitter. We show that any nilpotent group in dimension $n\leq 6$ has a corresponding Ricci nilsoliton black hole solution in dimension (n+2). Furthermore, we show that in dimensions (n+2)>8, there exists an infinite number of locally distinct Ricci nilsoliton black hole metrics.

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