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In order to investigate formation of relativistic jets at the center of aprogenitor of a long gamma-ray burst (GRB), we develop a two-dimensionalgeneral relativistic magnetohydrodynamic (GRMHD) code. We show the code passesmany, well-known test calculations, by which the reliability of the code isconfirmed. Then we perform a numerical simulation of a collapsar using arealistic progenitor model. It is shown that a jet is launched from the centerof the progenitor. We also find that the mass accretion rate after the launchof the jet shows rapid time variability that resembles to a typical timeprofile of a GRB. The structure of the jet is similar to the previous study: apoynting flux jet is surrounded by a funnel-wall jet. Even at the final stageof the simulation, bulk Lorentz factor of the jet is still low, and totalenergy of the jet is still as small as 10^48 erg. However, we find that theenergy flux per unit rest-mass flux is as high as 10^2 at the bottom of thejet. Thus we conclude that the bulk Lorentz factor of the jet can bepotentially high when it propagates outward. It is shown that the outgoingpoynting flux exists at the horizon around the polar region, which proves thatthe Blandford-Znajek mechanism is working. However, we conclude that the jet islaunched mainly by the magnetic field amplified by the gravitational collapseand differential rotation around the black hole, rather than theBlandford-Znajek mechanism.

Development of General Relativistic Magnetohydrodynamic Code and its Application to Central Engine of Long Gamma-Ray Bursts