  Modified Newtonian Dynamics is an empirical modification to Poisson's
equation which has had success in accounting for the `gravitational field'
$\Phi$ in a variety of astrophysical systems. The field $\Phi$ may be
interpreted in terms of the weak field limit of a variety of spacetime
geometries. Here we consider three of these geometries in a more comprehensive
manner and look at the effect on timelike and null geodesics. In particular we
consider the Aquadratic Lagrangian (AQUAL) theory, Tensor-Vector-Scalar (TeVeS)
theory and Generalized Einstein-{\AE}ther (GEA) theory. We uncover a number of
novel features, some of which are specific to the theory considered while
others are generic. In the case of AQUAL and TeVeS theories, the spacetime
exhibits an excess (AQUAL) or deficit (TeVeS) solid angle akin to the case of a
Barriola-Vilenkin global monopole. In the case of GEA, a disformal symmetry of
the action emerges in the limit of $\grad\Phi\rightarrow 0$. Finally, in all
theories studied, massive particles can never reach spatial infinity while
photons can do so only after experiencing infinite redshift.
