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Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetictheories where the quasiparticles are distributed uniformly in space, and theequilibration involves only their velocity distribution. For such solutions,the hydrodynamic variables remain constant. We construct asymptotically AdSsolutions of Einstein's gravity dual to such processes at strong coupling,perturbatively in the amplitude expansion, where the expansion parameter is theratio of the amplitude of the non-hydrodynamic shear-stress tensor to thepressure. At each order, we sum over all time derivatives through exactrecursion relations. We argue that the metric has a regular future horizon,order by order in the amplitude expansion, provided the shear-stress tensorfollows an equation of motion. At the linear order, this equation of motionimplies that the metric perturbations are composed of zero wavelengthquasinormal modes. Our method allows us to calculate the non-linear correctionsto this equation perturbatively in the amplitude expansion. We thus derive aspecial case of our previous conjecture on the regularity condition on theboundary stress tensor that endows the bulk metric with a regular futurehorizon, and also refine it further. We also propose a new outlook forheavy-ion phenomenology at RHIC and ALICE.

Homogeneous Relaxation at Strong Coupling from Gravity