  We develop a variational principle that extends the notion of a shearless
transport barrier from steady to general unsteady two-dimensional flows and
maps defined over a finite time interval. This principle reveals that
hyperbolic Lagrangian Coherent Structures (LCSs) and parabolic LCSs (or jet
cores) are the two main types of shearless barriers in unsteady flows. Based on
the boundary conditions they satisfy, parabolic barriers are found to be more
observable and robust than hyperbolic barriers, confirming widespread numerical
observations. Both types of barriers are special null-geodesics of an
appropriate Lorentzian metric derived from the Cauchy--Green strain tensor.
Using this fact, we devise an algorithm for the automated computation of
parabolic barriers. We illustrate our detection method on steady and unsteady
non-twist maps and on the aperiodically forced Bickley jet.
