We still want a relativistic extension of MOND. Such a theory is needed for conceptual completion of the MOND idea. But, it is doubly needed because we already have observed relativistic phenomena that show mass discrepancies, and we must ascertain that there too the culprit is not dark matter but modified dynamics.

Because of the
near values of *a*_{0} and the Hubble acceleration, there
are no local black holes that are in the MOND regime. The only system
that is strongly general relativistic and in the MOND regime is the
Universe at large. This, however means that we would need a
relativistic extension of MOND to describe cosmology. In fact, as
I have indicated, MOND itself may derive from cosmology, so it is
possible that the two problems will have to be tackled together as
parts and parcels of a unified concept. And, because the
cosmological expansion is strongly coupled with the process of
structure formation this too will have to await a modified
relativistic dynamics for its treatment.

Several relativistic theories incorporating the MOND principle have been discussed in the literature, but none is wholly satisfactory (see, e.g. [Bekenstein & Milgrom (1984)], [Bekenstein 1988], [Sanders 1997], and references therein).

There have also been attempts to supplement MOND with extra assumptions that will enable the study of structure formation, so as to get some glimpse of structure formation in MOND. For these see [Milgrom (1989)], [Sanders (2001)], and [Nusser (2001)].

Gravitational light deflection, and lensing, is another phenomenon
that requires modified relativistic dynamics. It is tempting to
take as a first approximation the deflection law of post-Newtonian
General Relativity with a potential that is the non-relativistic
MOND potential (see e.g. analyzes by
[Qin & al 1995], and
[Mortlock &
Turner 2001]
based on this assumption). This, however, is in no
way guaranteed. In GR this is only a post-Newtonian approximation,
and perhaps it would turn out to be a post-Newtonian approximation
of MOND (i.e. an approximation of MOND in the almost Newtonian,
*a* > > *a*_{0} regime). But, there is no reason
to assume that it is
correct in the deep-MOND regime. Even in the framework of this
assumption one needs to exercise care. For example, the thin-lens
hypothesis, by which it is a good approximation to assume that all
deflecting masses are projected on the same plane perpendicular to
the line of sight, breaks down in MOND. For example, *n* masses,
*M*, arranged along the line of sight (at inter-mass distances
larger that the impact parameter) bend light by a factor
*n*^{1/2} more than a single mass *nM*.

Also note that we may expect surprises in mondified inertia where we cannot even speak of the modified, MOND potential, as alluded to above.