C-metric like vacuum with non-negative cosmological constant in five dimensions

TL;DR

This paper introduces an exact five-dimensional vacuum solution with a non-negative cosmological constant, featuring acceleration horizons and a static region, analyzed through detailed geometric and global structure examination.

Contribution

It presents a novel 5D vacuum solution with a C-metric-like form, including detailed analysis of horizons and global structure, and offers a geometric interpretation in the zero cosmological constant case.

Findings

The solution has no black hole horizons but features acceleration horizons.

The spacetime admits a Kaluza-Klein reduction to 4D Einstein gravity with additional fields.

The metric's global structure and horizon geometry are thoroughly characterized.

Abstract

We present and analyze an exact 5-dimensional vacuum solution of Einstein equation with non-negative cosmological constant written in a C-metric like coordinate. The metric does not contain any black hole horizons in it, but has two acceleration horizons and a static patch in between. The coordinate system, horizon geometry and global structures are analyzed in detail, and in the case of vanishing cosmological constant, a simple exterior geometric interpretation is given. The metric possesses a spacelike Killing coordinate $\phi$ besides the timelike coordinate $t$, along which the spacetime can be dimensionally reduced via Kaluza-Klein mechanism and interpreted as Einstein gravity coupled to a 4 dimensional Liouville field (and a Maxwell field as well if a boost operation is performed before the Kaluza-Klein reduction).