  We construct supersymmetric brane solutions in string and M-theory with moduli parameters that depend arbitrarily on the light-cone time. Our investigation aims in understanding time dependent phenomena in gauge theories at strong coupling within the gauge/gravity correspondence. For that reason we use, as a basic ingredient, multicenter supergravity solutions which model the Coulomb branch of the corresponding strongly coupled gauge theories. We introduce the notion of shape invariant motions and show that in a particular limit involving pulse-type motions of finite energy, the solutions represent gravitational shock waves moving on the brane background geometry. We apply the general formalism for D3-branes distributed on a disc and on a sphere as well as for NS5-branes distributed on a ring, all with time varying radii. We examine the problem of open strings attached on moving branes and suggest a mechanism which may be responsible for giving rise at a macroscopic level to gravitational shock waves. 
Fundamental branes and shock waves