In 2011 Blanchet and Marsat suggested a fully relativistic version of
Milgrom's modified Newtonian dynamics (MOND) in which the dynamical degrees of
freedom consist of the spacetime metric and a foliation of spacetime, the
khronon field. This theory is simpler than the alternative relativsitic
formulations. We show that the theory has a consistent non-relativistic or slow
motion limit. Blanchet and Marsat showed that in the slow motion limit the
theory reproduces stationary solutions of modified Newtonian dynamics. We show
that these solutions are stable to khronon perturbations in the low
acceleration regime, for the cases of spherical, cylindrical and planar
symmetry. For non-stationary systems in the low acceleration regime we show
that the khronon field generally gives an order unity correction to the
modified Newtonian dynamics.Comment: v2: Error in discussion of previous work corrected, discussion of
khronon dynamics expanded, other minor corrections. v3: minor corrections and
clarification