  Results from the first fully general relativistic numerical simulations in
axisymmetry of a system formed by a black hole surrounded by a self-gravitating
torus in equilibrium are presented, aiming to assess the influence of the torus
self-gravity on the onset of the runaway instability. We consider several
models with varying torus-to-black hole mass ratio and angular momentum
distribution orbiting in equilibrium around a non-rotating black hole. The tori
are perturbed to induce the mass transfer towards the black hole. Our numerical
simulations show that all models exhibit a persistent phase of axisymmetric
oscillations around their equilibria for several dynamical timescales without
the appearance of the runaway instability, indicating that the self-gravity of
the torus does not play a critical role favoring the onset of the instability,
at least during the first few dynamical timescales.
