Global stability of self-gravitating disks in modified gravity
  We study the global stability of a self-gravitating disk in the context of
Modified Gravity (MOG) using N-body simulations. This theory is a relativistic
scalar-tensor-vector theory of gravity and presented to address the dark matter
problem. In the weak field limit MOG possesses two free parameters $\alpha$ and
$\mu_0$ which have been already determined using rotation curve data of spiral
galaxies. The evolution of a stellar self-gravitating disk and more
specifically the bar instability in MOG is investigated and compared to a
Newtonian case. Our models have exponential and Mestel-like surface densities
as $\Sigma\propto \exp(-r/h)$ and $\Sigma\propto 1/r$. It is found out that,
surprisingly, the disks are more stable against the bar mode in MOG than in
Newtonian gravity. In other words, the bar growth rate is effectively slower
than the Newtonian disks. Also we show that both free parameters, i.e. $\alpha$
and $\mu_0$, have stabilizing effects. In other words, increase in these
parameters will decrease the bar growth rate.
