Asymptotic flatness in higher dimensions

TL;DR

This paper investigates the asymptotic properties of higher-dimensional Myers-Perry metrics, establishing their conformal completion at spacelike infinity and analyzing the associated asymptotic symmetries, with results optimal in even dimensions.

Contribution

It demonstrates the conformal completion of Myers-Perry metrics at spacelike infinity in higher dimensions and characterizes their asymptotic symmetries, revealing optimal regularity in even dimensions.

Findings

Myers-Perry metrics have $C^{n-3,1}$ conformal completion at spacelike infinity.

The asymptotic symmetries associated with these metrics are characterized.

The regularity result is proven to be optimal in even spacetime dimensions.

Abstract

We show that $(n+1)$-dimensional Myers-Perry metrics, $n\geq4$, have a conformal completion at spacelike infinity of $C^{n-3,1}$ differentiability class, and that the result is optimal in even spacetime dimensions. The associated asymptotic symmetries are presented.