On Lovelock vacuum solution

TL;DR

This paper demonstrates that in higher dimensions, all Lovelock vacuum and electrovac solutions with a cosmological constant asymptotically behave like Einstein solutions, regardless of the Lovelock order.

Contribution

It establishes the universal asymptotic behavior of Lovelock solutions, showing independence from the polynomial order in large-distance limits.

Findings

Lovelock solutions asymptotically match Einstein solutions in high dimensions.

The asymptotic behavior is independent of the Lovelock polynomial order.

This universality holds for vacuum and electrovac solutions with a cosmological constant.

Abstract

We show that the asymptotic large $r$ limit of all Lovelock vacuum and electrovac solutions with $\Lambda$ is always the Einstein solution in $d \geq 2n+1$ dimensions. It is completely free of the order $n$ of the Lovelock polynomial indicating universal asymptotic behaviour.