Asymptotics with a cosmological constant: The solution space

TL;DR

This work derives the most general Newman–Penrose solution space for spacetimes with a cosmological constant and determines the residual gauge transformations preserving it. It reveals Λ modifies the asymptotic structure, fixing certain data while leaving two boundary functions, P and Q, as free radiation data, and shows the asymptotic symmetry is Diff(S^2) with a third class rotation rather than Bondi-type supertranslations. In the flat limit, the solution space reduces to a larger NU-type structure when the boundary metric is not constrained to be conformally flat; the results bridge NP and metric approaches in (A)dS contexts and illuminate how radiation and symmetries behave with a cosmological constant. The findings have potential implications for soft graviton theorems and holographic perspectives in asymptotically (A)dS settings.

Abstract

In this work, the solution space in the Newman-Penrose formalism with a cosmological constant is derived. The residual gauge transformation preserving the solution space is also worked out. By turning off the cosmological constant, the solution space has a well-defined flat limit. The asymptotic symmetry group of the resulting solution space consists of Diff($S^2$) transformations and supertranslations.