Relationship between Bondi-Sachs quantities and source of gravitational radiation in asymptotically de Sitter spacetime

TL;DR

This work clarifies how Bondi-Sachs (BS) quantities in asymptotically de Sitter spacetimes with a positive cosmological constant Λ can be expressed directly in terms of the source's quadrupole moments. It accomplishes this by transforming linearized Einstein-wave solutions with Λ first to the transverse-traceless gauge and then into BS coordinates using a new outgoing boundary condition. The authors derive explicit relationships between BS data and source quadrupoles (including both mass and pressure quadrupoles) for axisymmetric and general spacetimes, and discuss the practical impact, showing Λ effects are negligible for current GW detectors except at unrealistically large distances or extremely low frequencies. The results provide a bridge between source dynamics and asymptotic BS structure in a Λ-filled universe and extend prior Minkowski-limit findings to asymptotically de Sitter spacetimes.

Abstract

Gravitational radiation plays an important role in astrophysics. Based on the fact that our universe is expanding, the gravitational radiation when a positive cosmological constant is presented has been studied along with two different ways recently, one is the Bondi-Sachs (BS) framework in which the result is shown by BS quantities in the asymptotic null structure, the other is the perturbation approach in which the result is presented by the quadrupoles of source. Therefore, it is worth to interpret the quantities in asymptotic null structure in terms of the information of the source. In this paper, we investigate this problem and find the explicit expressions of BS quantities in terms of the quadrupoles of source in asymptotically de Sitter spacetime. We also estimate how far away the source is, the cosmological constant may affect the detection of the gravitational wave.