On the collision of two shock waves in AdS5
Daniel Grumiller, Paul Romatschke
TL;DR
Two ultrarelativistic shock waves in AdS5 are modeled to probe far-from-equilibrium dynamics in a strongly coupled gauge theory via gauge/gravity duality. By reformulating the post-collision metric in Rosen coordinates and applying holographic renormalization, the boundary energy-momentum tensor is extracted and shown to be conserved and traceless, though explicitly non-boost-invariant at early times. The analysis finds that the energy-momentum tensor components grow with proper time and reveals a negative longitudinal pressure, leading to a crude estimate of the thermalization time scaling as tau_therm ~ mu^{-1/3}. The work elucidates real-time, far-from-equilibrium dynamics in strongly coupled plasmas, highlighting the role of transverse dynamics and gauge choices, and points to future numerical and transverse-geometry extensions to refine thermalization predictions.
Abstract
We consider two ultrarelativistic shock waves propagating and colliding in five-dimensional Anti-de-Sitter spacetime. By transforming to Rosen coordinates, we are able to find the form of the metric shortly after the collision. Using holographic renormalization, we calculate the energy-momentum tensor on the boundary of AdS space for early times after the collision. Via the gauge-gravity duality, this gives some insights on bulk dynamics of systems created by high energy scattering in strongly coupled gauge theories. We find that Bjorken boost-invariance is explicitely violated at early times and we obtain an estimate for the thermalization time in this simple system.