  We study local variations of causal curves in a space-time with respect to
b-length (or generalised affine parameter length). In a convex normal
neighbourhood, causal curves of maximal metric length are geodesics. Using
variational arguments, we show that causal curves of minimal b-length in
sufficiently small globally hyperbolic sets are geodesics. As an application we
obtain a generalisation of a theorem by B. G. Schmidt, showing that the cluster
curve of a partially future imprisoned, future inextendible and future
b-incomplete curve must be a null geodesic. We give examples which illustrate
that the cluster curve does not have to be closed or incomplete. The theory of
variations developed in this work provides a starting point for a Morse theory
of b-length.
