de Sitter Static Black Ring in Large $D$ Membrane Paradigm at the Second Order

TL;DR

This paper derives static de Sitter black ring solutions using the second order large D membrane paradigm, extending previous first order results and satisfying equilibrium conditions for thin rings.

Contribution

It presents the first derivation of static de Sitter black rings at second order in the large D membrane paradigm, bridging a gap in previous first order analyses.

Findings

Static de Sitter black ring solutions obtained at second order.

Solutions satisfy equilibrium conditions for thin rings.

Extends the applicability of the membrane paradigm to more complex black objects.

Abstract

It was shown in arXiv:2006.16163 that the effective stationary membrane equations from the large $D$ membrane paradigm at the first order admit black ring solutions in flat and AdS cases, but the de Sitter solution obtained in arXiv:0806.1954 lies outside the domain of their applicability. In this short note the static de Sitter black ring is obtained from the second order membrane paradigm, and it satisfies the equilibrium condition for the thin ring solution of arXiv:0806.1954. This provides a segue into the stationary black rings at the second order.