3 Numerical Simulations

By the year 2010, five groups – AEI, CCCW, KT, LBPLI, and UIUC groups – have succeeded in fully general-relativistic simulations for BH-NS binaries and provided a variety of the numerical results. The results of these groups agree qualitatively with each other and have clarified the basic picture for the merger and tidal disruption processes, although quantitatively, minor differences (e.g., on the remnant disk mass) have been reported. They have provided the criteria for tidal disruption, the final mass and spin of the BH left after the merger, the remnant disk mass, gravitational waveforms, and gravitational-wave spectrum. In the following sections, we review the methods of numerical relativity employed in these groups, the basic picture of the merger and tidal disruption processes clarified to date, and the resulting gravitational waveforms and spectra, separately.

 3.1 Numerical method
  3.1.1 Initial condition
  3.1.2 Evolving metric
  3.1.3 Evolving a black hole
  3.1.4 Hydrodynamics
  3.1.5 Equations of state
  3.1.6 Adaptive mesh refinement
 3.2 Current parameter space surveyed
 3.3 Merger process
  3.3.1 Zero BH spin
  3.3.2 Nonzero BH spin
  3.3.3 Extent of remnant disk
  3.3.4 Effects of EOS
 3.4 Properties of the remnant black hole and disk
 3.5 Criteria for tidal disruption
 3.6 Gravitational waveforms
  3.6.1 Zero BH spin
  3.6.2 Nonzero BH spin
 3.7 The Fourier spectrum of gravitational waves
  3.7.1 Zero BH-spin case
  3.7.2 Non-zero BH-spin case
 3.8 Summary and issues for the near future

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