The fate of bound systems through Sudden Future Singularities
  Sudden singularities occur in FRW spacetimes when the scale factor remains
finite and different from zero while some of its derivatives diverge. After
proper rescaling, the scale factor close to such a singularity at $t=0$ takes
the form $a(t)=1+ c |t|^\eta$ (where $c$ and $\eta$ are parameters and
$\eta\geq 0$). We investigate analytically and numerically the geodesics of
free and gravitationally bound particles through such sudden singularities. We
find that even though free particle geodesics go through sudden singularities
for all $\eta\geq 0$, bound systems get dissociated for a wide range of the
parameter $c$. For $\eta <1$ bound particles receive a diverging impulse at the
singularity and get dissociated for all positive values of the parameter $c$.
For $\eta > 1$ (Sudden Future Singularities (SFS)) bound systems get a finite
impulse that depends on the value of $c$ and get dissociated for values of $c$
larger than a critical value $c_{cr}(\eta,\omega_0)>0$ that increases with the
value of $\eta$ and the rescaled angular velocity $\omega_0$ of the bound
system. We obtain an approximate equation for the analytical estimate of
$c_{cr}(\eta,\omega_0)$. We also obtain its accurate form by numerical
derivation of the bound system orbits through the singularities. Bound system
orbits through Big Brake singularities ($c<0$, $1<\eta<2$) are also derived
numerically and are found to get disrupted at the singularity. However, they
remain bound for all values of the parameter $c$ considered.
