Central MONDian spike in spherically symmetric systems
  Under a MONDian view, astrophysical systems are expected to follow Newtonian
dynamics whenever the local acceleration is above the critical $a_{0}=1.2
\times 10^{-10} m s^{-2}$, and enter a modified regime for accelerations below
this critical value. Indeed, the dark matter phenomenology on galactic and
subgalactic scales appears always, and only, at low accelerations. It is
standard to find the $a<a_{0}$ regime towards the low density outskirts of
astronomical systems, where under a Newtonian interpretation, dark matter
becomes conspicuous. Thus, it is standard to find, and to think, of the dense
central regions of observed systems as purely Newtonian. However, under
spherical symmetry in the MONDian as in the Newtonian case, the local
acceleration will tend to zero as one approaches the very centre of a mass
distribution. It is clear that for spherically symmetric systems, an inner
$a<a_{0}$ region will necessarily appear interior to a critical radius which
will depend on the details of the density profile in question. Here we
calculate analytically such a critical radius for a constant density core, and
numerically for a cored isothermal profile. Under a Newtonian interpretation,
such a central MONDian region will be interpreted as extra mass, analogous to
the controversial black holes sometimes inferred to lie at the centres of
globular clusters, despite an absence of nuclear activity detected to date. We
calculate this effect and give predictions for the "central black hole" mass to
be expected under Newtonian interpretations of low density Galactic globular
clusters.
