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Axisymmetric numerical simulations of rotating stellar core collapse to aneutron star are performed in the framework of full general relativity. Theso-called Cartoon method, in which the Einstein field equations are solved inthe Cartesian coordinates and the axisymmetric condition is imposed around the$y=0$ plane, is adopted. The hydrodynamic equations are solved in thecylindrical coordinates (on the $y=0$ plane in the Cartesian coordinates) usinga high-resolution shock-capturing scheme with the maximum grid size$(2500,2500)$. A parametric equation of state is adopted to model collapsingstellar cores and neutron stars following Dimmelmeier et al. It is found thatthe evolution of central density during the collapse, bounce, and formation ofprotoneutron stars agree well with those in the work of Dimmelmeier et al. inwhich an approximate general relativistic formulation is adopted. Thisindicates that such approximation is appropriate for following axisymmetricstellar core collapses and subsequent formation of protoneutron stars.Gravitational waves are computed using a quadrupole formula. It is found thatthe waveforms are qualitatively in good agreement with those by Dimmelmeier etal. However, quantitatively, two waveforms do not agree well. Possible reasonsfor the disagreement are discussed.Comment: Phys. Rev. D in pres

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