Abstract
The trajectories of idealised (zero-thickness) cosmic strings in flat space-time typically contain isolated points, known as cusps, where the local radius of curvature of the string goes to zero. It has long been known that the weak-field approximation breaks down in the vicinity of a cusp, leading to a beam of gravitational radiation directed parallel to the motion of the cusp. In this paper I show that the weak-field approximation also breaks down in a region with radius of order (G\mu )^2 L and enclosed mass of order (G\mu) M, where L is the length of the string, M is its total mass, and \mu is its mass per unit length. I further indicate how a self-consistent analysis of the effects of a cusp within the full framework of general relativity might be performed.