Toward the AdS/CFT gravity dual for high energy collisions. I. Falling into the AdS space

In the context of the AdS/CFT correspondence we discuss the gravity dual of a high energy collision in a strongly coupled N=4 SYM gauge theory. We suggest a setting in which two colliding objects are made of nondynamical heavy quarks and antiquarks, which allows one to treat the process in classical string approximation. Collision debris consist of closed as well as open strings. If the latter have ends on two outgoing charges, they are being stretched along the collision axes. We discuss motion in AdS of some simple objects first-massless and massive particles-and then focus on open strings. We study the latter in considerable detail, concluding that they rapidly become rectangular in proper time-spatial rapidity tau - y coordinates with well separated fragmentation part and a near-free-falling rapidity-independent central part. Assuming that in the collisions of walls of charges multiple stretching strings are created, we also consider the motion of a 3D stretching membrane. We then argue that a complete solution can be approximated by two different vacuum solutions of Einstein equations, with matter membrane separating them. We identify one of these solutions with a Janik-Peschanski stretching black hole solution, and show that all objects approach its (retreating) horizon in a universal manner.