  Neutron stars (NSs) in the astrophysical universe are often surrounded by
accretion disks. Accretion of matter onto an NS may increase its mass above the
maximum value allowed by its equation of state, inducing its collapse to a
black hole (BH). Here we study this process for the first time, in
three-dimensions, and in full general relativity. By considering three initial
NS configurations, each with and without a surrounding disk (of mass ~7%
M_{NS}), we investigate the effect of the accretion disk on the dynamics of the
collapse and its imprint on both the gravitational wave (GW) and
electromagnetic (EM) signals that can be emitted by these sources. We show in
particular that, even if the GW signal is similar for the accretion induced
collapse (AIC) and the collapse of an NS in vacuum (and detectable only for
Galactic sources), the EM counterpart could allow us to discriminate between
these two types of events. In fact, our simulations show that, while the
collapse of an NS in vacuum leaves no appreciable baryonic matter outside the
event horizon, an AIC is followed by a phase of rapid accretion of the
surviving disk onto the newly formed BH. The post-collapse accretion rates, on
the order of ~10^{-2} M_{sun} s^{-1}, make these events tantalizing candidates
as engines of short gamma-ray bursts.
