Asymptotics with a positive cosmological constant: IV. The `no-incoming radiation' condition

Understand

Consider compact objects --such as neutron star or black hole binaries-- in \emph{full, non-linear} general relativity.

• In the case with zero cosmological constant $\Lambda$, the gravitational radiation emitted by such systems is described by the well established, 50+ year old framework due to Bondi, Sachs, Penrose and others.
• However, so far we do not have a satisfactory extension of this framework to include a \emph{positive} cosmological constant --or, more generally, the dark energy responsible for the accelerated expansion of the universe.
• In particular, we do not yet have an adequate gauge invariant characterization of gravitational waves in this context.