Gravitational multipole moments for asymptotically de Sitter spacetimes

TL;DR

This paper introduces a new method to compute gravitational multipole moments for objects in asymptotically de Sitter spacetimes, extending previous definitions and applying it to Kerr-de Sitter black holes.

Contribution

It develops a prescription based on Noether charges and multipole symmetries for asymptotically de Sitter spacetimes, including explicit calculations for Kerr-de Sitter black holes.

Findings

Derived multipole symmetries for asymptotically de Sitter spacetimes.

Applied the method to Kerr-de Sitter black holes.

Recovered Geroch-Hansen moments in the limit of zero cosmological constant.

Abstract

We provide a prescription to compute the gravitational multipole moments of compact objects for asymptotically de Sitter spacetimes. Our prescription builds upon a recent definition of the gravitational multipole moments in terms of Noether charges associated to specific vector fields, within the residual harmonic gauge, dubbed multipole symmetries. We first derive the multipole symmetries for spacetimes which are asymptotically de Sitter; we also show that these symmetry vector fields eliminate the non-propagating degrees of freedom from the linearized gravitational wave equation in a suitable gauge. We then apply our prescription to the Kerr-de Sitter black hole and compute its multipole structure. Our result recovers the Geroch-Hansen moments of the Kerr black hole in the limit of vanishing cosmological constant.