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Binary neutron-star systems represent primary sources for the gravitational-wave detectors that are presently operating or are close to being operating at the target sensitivities. We present a systematic investigation in full general relativity of the dynamics and gravitational-wave emission from binary neutron stars which inspiral and merge, producing a black hole surrounded by a torus. Our results represent the state of the art from several points of view: (i) We use high-resolution shock-capturing methods for the solution of the hydrodynamics equations and high-order finite-differencing techniques for the solution of the Einstein equations; (ii) We employ adaptive mesh-refinement techniques with “moving boxes” that provide high-resolution around the orbiting stars; (iii) We use as initial data accurate solutions of the Einstein equations for a system of binary neutron stars in irrotational quasicircular orbits; (iv) We exploit the isolated-horizon formalism to measure the properties of the black holes produced in the merger; (v) Finally, we use two approaches, based either on gauge-invariant perturbations or on Weyl scalars, to calculate the gravitational waves emitted by the system. Within our idealized treatment of the matter, these techniques allow us to perform accurate evolutions on time scales never reported before (i.e. ~30 ms) and to provide the first complete description of the inspiral and merger of a neutron-star binary leading to the prompt or delayed formation of a black hole and to its ringdown. We consider either a polytropic equation of state or that of an ideal fluid and show that already with this idealized treatment a very interesting phenomenology can be described. In particular, we show that while higher-mass polytropic binaries lead to the prompt formation of a rapidly rotating black hole surrounded by a dense torus, lower-mass binaries give rise to a differentially rotating star, which undergoes large oscillations and emits large amounts of gravitational radiation. Eventually, also the hyper-massive neutron star collapses to a rotating black hole surrounded by a torus. Finally, we also show that the use of a nonisentropic equation of state leads to significantly different evolutions, giving rise to a delayed collapse also with high-mass binaries, as well as to a more intense emission of gravitational waves and to a geometrically thicker torus.
