Ricci Nilsoliton Black Holes

Abstract

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.