# Asymptotically simple spacetimes and mass loss due to gravitational waves

## TL;DR

This paper reviews recent progress and open problems in understanding the structure of asymptotically simple spacetimes with a positive cosmological constant, focusing on mass loss due to gravitational waves in de Sitter-like universes.

## Contribution

It consolidates various approaches to extending the concept of Bondi mass in universes with positive cosmological constant and discusses future research directions.

## Key findings

- Conformal structure of spacetime depends on the sign of b3b4.
- Progress has been made in linear and Hamiltonian formulations.
- Open problems remain in defining mass loss in b3b4>0 universes.

## Abstract

The cosmological constant $\Lambda$ used to be a freedom in Einstein's theory of general relativity, where one had a proclivity to set it to zero purely for convenience. The signs of $\Lambda$ or $\Lambda$ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on $\Lambda$: null infinity $\mathcal{I}$ is a spacelike, null, or timelike hypersurface, if $\Lambda>0$, $\Lambda=0$, or $\Lambda<0$, respectively. Recent observations of distant supernovae have taught us that our universe expands at an accelerated rate, and this can be accounted for by choosing $\Lambda>0$ in Einstein's theory of general relativity. A quantity that depends on the conformal structure of spacetime, especially on the nature of $\mathcal{I}$, is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with $\Lambda>0$ has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearisation, attempts using a Hamiltonian formulation based on "linearised" asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.