  Using the asymptotic form of the bulk Weyl tensor, we present an explicit
approach that allows us to reconstruct exact four-dimensional Einstein
spacetimes which are algebraically special with respect to Petrov's
classification. If the boundary metric supports a traceless, symmetric and
conserved complex rank-two tensor, which is related to the boundary Cotton and
energy-momentum tensors, and if the hydrodynamic congruence is shearless, then
the bulk metric is exactly resummed and captures modes that stand beyond the
hydrodynamic derivative expansion. We illustrate the method when the congruence
has zero vorticity, leading to the Robinson-Trautman spacetimes of arbitrary
Petrov class, and quote the case of non-vanishing vorticity, which captures the
Plebanski-Demianski Petrov D family.
