Novel accelerating Einstein vacua and smooth inhomogeneous Riemannian manifolds

TL;DR

This paper introduces a new class of Einstein vacuum solutions with a positive cosmological constant, featuring accelerating horizons and smooth, inhomogeneous Riemannian manifolds that generalize known gravitational instantons.

Contribution

It presents a novel class of Einstein vacua with non-zero cosmological constant and inhomogeneous, smooth Riemannian manifolds, extending the landscape of gravitational instantons.

Findings

Solutions have non-vanishing cosmological constant and accelerating horizons.

Euclideanized solutions are smooth, compact, and inhomogeneous.

Analogous to Don Page's gravitational instanton.

Abstract

A novel class of Einstein vacua is presented, which possess non-vanishing cosmological constant and accelerating horizon with the topology of $S^{D-3}$ fibration over $S^{1}$. After Euclideanization, the solution describes a conformally distorted $S^{D-1}$ fibration over $S^1$, which is smooth, compact and inhomogeneous, and can be regarded as analogue of Don Page's gravitational instanton.