Gravitational waves from axisymmetric rotating stellar core collapse to a neutron star in full general relativity

Axisymmetric numerical simulations of rotating stellar core collapse to a neutron star are performed in the framework of full general relativity. The so-called Cartoon method, in which the Einstein field equations are solved in Cartesian coordinates and the axisymmetric condition is imposed around the $y=0$ plane, is adopted. The hydrodynamic equations are solved in cylindrical coordinates (on the $y=0$ plane in Cartesian coordinates) using a high-resolution shock-capturing scheme with maximum grid size $(2500,2500).$ A parametric equation of state is adopted to model collapsing stellar cores and neutron stars following Dimmelmeier, Font, and M\"uller. It is found that the evolution of the central density during the collapse, bounce, and formation of protoneutron stars agrees well with that in the work of Dimmelmeier, Font, and M\"uller in which an approximate general relativistic formulation is adopted. This indicates that such an approximation is appropriate for following axisymmetric stellar core collapses and the subsequent formation of protoneutron stars. Gravitational waves are computed using a quadrupole formula. It is found that the waveforms are qualitatively in good agreement with those by Dimmelmeier, Font, and M\"uller. However, quantitatively, two waveforms do not agree well. The possible reasons for the disagreement are discussed.

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