The asymptotics of stationary electro-vacuum metrics in odd space-time dimensions

TL;DR

This paper proves that stationary electro-vacuum solutions in odd-dimensional space-times higher than seven are analytic at spatial infinity, with additional results for static vacuum solutions in five dimensions, enhancing understanding of their mathematical structure.

Contribution

It establishes analyticity of stationary electro-vacuum solutions in higher odd dimensions and extends results to static vacuum solutions in five dimensions.

Findings

Stationary electro-vacuum solutions are analytic at spatial infinity in odd dimensions >7.

Static vacuum solutions in five dimensions are analytic at spatial infinity with non-zero mass.

Analyticity holds in a large family of gauges.

Abstract

We show that stationary, asymptotically flat solutions of the electro-vacuum Einstein equations are analytic at $i^0$, for a large family of gauges, in odd space-time dimensions higher than seven. The same is true in space-time dimension five for static vacuum solutions with non-vanishing mass.