(Abridged.) The accretion-induced collapse (AIC) of a white dwarf (WD) may lead to the formation of a protoneutron star and a collapse-driven supernova explosion. This process represents a path alternative to thermonuclear disruption of accreting white dwarfs in Type Ia supernovae. Neutrino and gravitational-wave (GW) observations may provide crucial information necessary to reveal a potential AIC. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic AIC simulations using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models in rotational equilibrium, with a wide range of rotational configurations, temperatures and central densities, we extend previous Newtonian studies and find that the GW signal has a generic shape akin to what is known as a Type III signal in the literature. We discuss the detectability of the emitted GWs, showing that the signal-to-noise ratio for current or next-generation interferometer detectors could be high enough to detect such events in our Galaxy. Some of our AIC models form massive quasi-Keplerian accretion disks after bounce. In rapidly differentially rotating models, the disk mass can be as large as ~0.8-Msun. Slowly and/or uniformly rotating models produce much smaller disks. Finally, we find that the postbounce cores of rapidly spinning white dwarfs can reach sufficiently rapid rotation to develop a nonaxisymmetric rotational instability.
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