Ricci Nilsoliton Black Holes

TL;DR

This paper constructs higher-dimensional black hole solutions with Ricci nilsoliton horizons, extending anti-de Sitter black holes, and explores their geometric properties and classifications.

Contribution

It introduces a method to generate Ricci nilsoliton black holes in various dimensions, expanding the known solutions beyond asymptotically AdS spacetimes.

Findings

Existence of Ricci nilsoliton black holes in dimensions up to 8.

Infinite family of solutions in dimensions greater than 8.

Black holes are asymptotically Einstein solvmanifolds, not AdS.

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.