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The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the ’60s. Recent findings from the observation of distant supernovae revealed that the rate of expansion of our universe is accelerating, which may be well explained by sticking a positive cosmological constant into the Einstein field equations for general relativity. By solving the Newman–Penrose equations (which are equivalent to the Einstein field equations), we generalize this notion of Bondi mass–energy and thereby provide a firm theoretical description of how an isolated gravitating system loses energy as it radiates gravitational waves, in a universe that expands at an accelerated rate. This is in line with the observational front of LIGO’s first announcement in February 2016 that gravitational waves from the merger of a binary black hole system have been detected.

The cosmological constant $\mathrm{\Lambda }$ used to be a freedom in Einstein’s theory of general relativity (GR), where one had a proclivity to set it to zero purely for convenience. The signs of $\mathrm{\Lambda }$ or $\mathrm{\Lambda }$ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on $\mathrm{\Lambda }$: null infinity ${ℐ}$ is a spacelike, null, or timelike hypersurface, if $\mathrm{\Lambda }>0$, $\mathrm{\Lambda }=0$, or $\mathrm{\Lambda }<0$, 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 $\mathrm{\Lambda }>0$ in Einstein’s theory of GR. A quantity that depends on the conformal structure of spacetime, especially on the nature of ${ℐ}$, 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 $\mathrm{\Lambda }>0$ has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearization, attempts using a Hamiltonian formulation based on “linearized” 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.

The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the ’60s. Recent findings from the observation of distant supernovae revealed that the rate of expansion of our universe is accelerating, which may be well explained by sticking a positive cosmological constant into the Einstein field equations for general relativity. By solving the Newman–Penrose equations (which are equivalent to the Einstein field equations), we generalize this notion of Bondi mass–energy and thereby provide a firm theoretical description of how an isolated gravitating system loses energy as it radiates gravitational waves, in a universe that expands at an accelerated rate. This is in line with the observational front of LIGO’s first announcement in February 2016 that gravitational waves from the merger of a binary black hole system have been detected.