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

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.