  Recently, a relativistic gravitation theory has been proposed [J. D.
Bekenstein, Phys. Rev. D {\bf 70}, 083509 (2004)] that gives the Modified
Newtonian Dynamics (or MOND) in the weak acceleration regime. The theory is
based on three dynamic gravitational fields and succeeds in explaining a large
part of extragalactic and gravitational lensing phenomenology without invoking
dark matter. In this work we consider the strong gravity regime of TeVeS. We
study spherically symmetric, static and vacuum spacetimes relevant for a
non-rotating black hole or the exterior of a star. Two branches of solutions
are identified: in the first the vector field is aligned with the time
direction while in the second the vector field has a non-vanishing radial
component. We show that in the first branch of solutions the \beta and \gamma
PPN coefficients in TeVeS are identical to these of general relativity (GR)
while in the second the \beta PPN coefficient differs from unity violating
observational determinations of it (for the choice of the free function $F$ of
the theory made in Bekenstein's paper). For the first branch of solutions, we
derive analytic expressions for the physical metric and discuss their
implications. Applying these solutions to the case of black holes, it is shown
that they violate causality (since they allow for superluminal propagation of
metric, vector and scalar waves) in the vicinity of the event horizon and/or
that they are characterized by negative energy density carried by the fields.
