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Modified Newtonian Dynamics is an empirical modification to Poissons 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 $gradPhirightarrow 0$. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.
Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to
Screened modified gravity (SMG) is a kind of scalar-tensor theories with screening mechanisms, which can generate screening effect to suppress the fifth force in high density environments and pass the solar system tests. Meanwhile, the potential of s
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous descript
Quantum gravity phenomenology suggests an effective modification of the general relativistic dispersion relation of freely falling point particles caused by an underlying theory of quantum gravity. Here we analyse the consequences of modifications of
We look for observational signatures that could discriminate between Newtonian and modified Newtonian (MOND) dynamics in the Milky Way, in view of the advent of large astrometric and spectroscopic surveys. Indeed, a typical signature of MOND is an ap