Addendum to 'Coherent Lagrangian vortices: the black holes of turbulence'

In Haller & Beron-Vera (J. Fluid Mech., vol. 731, 2013, R4) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null geodesics of the Lorentzian metric induced by a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here, we give an improved discussion of this analogy.