Researchers have investigated the existence of asymptotic gravitational radiation in pure-radiation Robinson-Trautman metrics, which describe "photon rockets" with point, string, and sheet sources. The study incorporates a cosmological constant (Λ) of arbitrary sign, extending previous work that focused on the Λ=0 case. The primary goal was to determine the conditions under which these systems emit or do not emit gravitational radiation at infinity, using the asymptotic super-Poynting vector as a criterion.

For point sources, it was confirmed that the Kinnersley rocket is the only one without gravitational radiation, a result already known for Λ=0 and which holds for Λ≠0. However, for string and sheet sources, the study reveals new configurations where gravitational radiation can be absent. This distinction between source types is crucial for understanding the dynamics of these systems in a universe with a cosmological constant.

The criteria for the absence of gravitational radiation differ depending on the sign of Λ. For Λ>0, the absence of radiation is characterized by the vanishing of the canonical asymptotic super-Poynting vector, computed with respect to the unit normal to scri (null infinity). In contrast, for Λ<0, the appropriate criterion is the vanishing of the components normal to scri of the asymptotic super-Poynting vectors associated with any unit timelike vector tangent to scri, or, equivalently, the proportionality between the Cotton-York tensor and the holographic stress tensor at scri. Explicit examples of metrics have been provided where these tensors commute, but gravitational radiation persists because they are not proportional. Furthermore, the principal null directions of the rescaled Weyl tensor at scri have been determined for both signs of Λ, relating their geometry to the tensorial criteria for gravitational radiation.