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

## TL;DR

This paper derives explicit relations between Bondi-Sachs quantities and source quadrupoles in asymptotically de Sitter spacetime, exploring how the cosmological constant influences gravitational wave detection.

## Contribution

It provides the first explicit expressions linking BS quantities to source quadrupoles in asymptotically de Sitter spacetime, enhancing understanding of gravitational radiation in expanding universes.

## Key findings

- Explicit formulas for BS quantities in terms of source quadrupoles
- Estimation of source distance considering cosmological constant effects
- Analysis of how de Sitter expansion impacts gravitational wave detection

## 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.