  Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic
theories where the quasiparticles are distributed uniformly in space, and the
equilibration involves only their velocity distribution. For such solutions,
the hydrodynamic variables remain constant. We construct asymptotically AdS
solutions of Einstein's gravity dual to such processes at strong coupling,
perturbatively in the amplitude expansion, where the expansion parameter is the
ratio of the amplitude of the non-hydrodynamic shear-stress tensor to the
pressure. At each order, we sum over all time derivatives through exact
recursion relations. We argue that the metric has a regular future horizon,
order by order in the amplitude expansion, provided the shear-stress tensor
follows an equation of motion. At the linear order, this equation of motion
implies that the metric perturbations are composed of zero wavelength
quasinormal modes. Our method allows us to calculate the non-linear corrections
to this equation perturbatively in the amplitude expansion. We thus derive a
special case of our previous conjecture on the regularity condition on the
boundary stress tensor that endows the bulk metric with a regular future
horizon, and also refine it further. We also propose a new outlook for
heavy-ion phenomenology at RHIC and ALICE.
