Finite momentum at string endpoints

We argue that classical strings, both bosonic and supersymmetric, can have finite energy and momentum at their endpoints. We show that in a general curved background, string endpoints must propagate along null geodesics as long as their energy remains finite. Finite endpoint momentum allows strings with a fixed energy to travel a greater distance in a five-dimensional anti-de Sitter Schwarzschild background than has been possible for classical solutions considered previously. We review the relevance to heavy ion phenomenology of the dependence of this distance on energy, and we propose a scheme for determining the instantaneous rate of energy loss.