A Note on the Positive Constant Curvature Space

TL;DR

This paper constructs a higher-dimensional positive constant curvature space with a cosmological horizon by identifying points along a Killing vector in de Sitter space, extending the Schwarzschild-de Sitter solution.

Contribution

It introduces a new higher-dimensional space with positive constant curvature and a specific topology, generalizing known solutions in de Sitter space.

Findings

Space has a cosmological event horizon.

Topology is ${\

M}_{D-1} imes S^1$.

Abstract

We construct a positive constant curvature space by identifying some points along a Killing vector in a de Sitter Space. This space is the counterpart of the three-dimensional Schwarzschild-de Sitter solution in higher dimensions. This space has a cosmological event horizon, and is of the topology ${\cal M}_{D-1}\times S^1$, where ${\cal M}_{D-1}$ denotes a $(D-1)$-dimensional conformal Minkowski spacetime.