Universal slow fall-off to the unique AdS infinity in Einstein-Gauss-Bonnet gravity

TL;DR

This paper proves that in higher-dimensional Einstein-Gauss-Bonnet gravity, the asymptotic behavior of spacetimes universally exhibits slow fall-off to the unique AdS infinity under certain conditions, extending understanding of AdS asymptotics.

Contribution

It establishes the conditions under which the slow fall-off to AdS infinity is universal in Einstein-Gauss-Bonnet gravity, including the role of fine-tuning and matter conditions.

Findings

Vanishing generalized Misner-Sharp mass implies maximally symmetric spacetime for  0 in  without fine-tuning.

Under fine-tuning, the spacetime is equivalent to vacuum class I.

Asymptotically AdS spacetime is a special case of vacuum class I, showing universal slow fall-off.

Abstract

In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant $\Lambda$. First, for $\Lambda\le 0$ and $\alpha \ge 0$ without a fine-tuning to give a unique anti-de Sitter vacuum, where $\alpha$ is the Gauss-Bonnet coupling constant, vanishing generalized Misner-Sharp mass is equivalent to the maximally symmetric spacetime. Under the fine-tuning, it is equivalent to the vacuum class I spacetime. Second, under the fine-tuning with $\alpha>0$, the asymptotically anti-de Sitter spacetime in the higher-dimensional Henneaux-Teitelboim sense is only a special class of the vacuum class I spacetime. The latter means the universal slow fall-off to the unique anti-de Sitter infinity in the presence of physically reasonable matter.