Five-dimensional vacuum Einstein spacetimes in C-metric like coordinates

TL;DR

This paper explores five-dimensional vacuum Einstein spacetimes with a C-metric-like coordinate system, analyzing their horizons, causal structures, and relations to standard vacua, and derives related four-dimensional solutions through dimensional reduction.

Contribution

It introduces a detailed analysis of 5D Einstein spacetimes in C-metric-like coordinates and connects them to known 4D Einstein-Maxwell-Liouville solutions via reduction.

Findings

Analysis of horizons and causal structures in 5D spacetimes.

Derivation of 4D Einstein-Maxwell-Liouville solutions from 5D models.

Connections established between higher-dimensional and standard 4D vacua.

Abstract

A 5-dimensional Einstein spacetime with (non)vanishing cosmological constant is analyzed in detail. The metric is in close analogy with the 4-dimensional massless uncharged C-metric in many aspects. The coordinate system, horizons and causal structures, relations to standard de Sitter, anti de Sitter and Minkowski vacua are investigated. After a boost and Kaluza-Klein reduction, we get an exact solution of 4-dimensional Einstein-Maxwell-Liouville theory which reduces to a solution to Einstein-Liouville theory in the limit of zero boost velocity and to that of Einstein-Maxwell-diliton theory in the case of zero cosmological constant.