Global structure of Robinson-Trautman radiative space-times with cosmological constant

Robinson-Trautman radiative space-times of Petrov type II with a nonvanishing cosmological constant $\Lambda$ and mass parameter $m>\mathrm{}0\mathrm{}$ are studied using analytical methods. They are shown to approach the corresponding spherically symmetric Schwarzschild–de Sitter or Schwarzschild–anti-de Sitter solution at large retarded times. Their global structure is analyzed, and it is demonstrated that the smoothness of the extension of the metrics across the horizon, as compared with the case $\Lambda =0\mathrm{}$, can increase for $\Lambda >0\mathrm{}$ and decreases for $\Lambda <0\mathrm{}$. For the extreme value $9\Lambda m^2=1\mathrm{}$, the extension is smooth but nonanalytic. This case appears to be the first example of a smooth but nonanalytic horizon. The models with $\Lambda >0\mathrm{}$ exhibit explicitly the cosmic no-hair conjecture under the presence of gravitational waves.