Horizon Formation in High-Energy Particles Collision

We investigate a classical formation of a trapped surface in 4-dimensional flat space-time in a process of a non-head-on collision of two high-energy particles which are treated as Aichelburg-Sexl shock waves. From the condition of the horizon volume local maximality an equation for the trapped surface is deduced. Using a known solution on the shocks we find a time-dependent solution describing the trapped surface between the shocks. We analyze the horizon appearance and evolution. Obtained results may describe qualitatively the horizon formation in higher dimensional space-time.