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 the Einstein equation with a negative cosmological constant and generalise therefore, Anti-de Sitter black hole spacetimes. The approach combines a work by Lauret–which relates the 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≤6 has a corresponding Ricci nilsoliton black hole solution in dimension (n+2). Furthermore, we show that in dimensions (n+2)>8, there exist an infinite number of locally distinct Ricci nilsoliton black hole metrics.