$lquot$Proper acceleration$rquot$ of a null geodesic in curved spacetime

Given a null geodesic in Minkowski spacetime, there exists a one-parameter family of observers in 'hyperbolic' motion which approaches the null geodesic as the parameter x 0 approaches zero. It is well known that the proper acceleration of the observers in the family approaches infinity as their world line approaches the null geodesic. The main purpose of this paper is to generalize this result to future-complete null geodesics in curved spacetimes.