I consider the class of AdS_4 Robinson-Trautman metrics and use them to explore aspects of non-equilibrium dynamics in the bulk as well as on the boundary in terms of geometric flows. This class of metrics illustrates non-trivially the validity of Penrore's
inequality as gravitational radiation is emitted from bounded sources and space-time equilibrates to a black-hole state. The holographic energy-momentum tensor is also obtained and comparison with black-hole hydrodynamics is made at late times, showing that there is entropy production. [Based on joint work with K. Skenderis, arXiv:1404.4824 [hep-th]]
