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A radiation-magnetohydrodynamic simulation for the black hole-torus system isperformed in the framework of full general relativity for the first time. Atruncated moment formalism is employed for a general relativistic neutrinoradiation transport. Several systems in which the black hole mass is $M_{\rmBH}=3$ or $6M_{\odot}$, the black hole spin is zero, and the torus mass is$\approx 0.14$--$0.38M_{\odot}$ are evolved as models of the remnant formedafter the merger of binary neutron stars or black hole-neutron star binaries.The equation of state and microphysics for the high-density andhigh-temperature matter are phenomenologically taken into account in asemi-quantitative manner. It is found that the temperature in the inner regionof the torus reaches $\agt 10$ MeV which enhances a high luminosity ofneutrinos $\sim 10^{51}$ ergs/s for $M_{\rm BH}=6M_{\odot}$ and $\sim 10^{52}$ergs/s for $M_{\rm BH}=3M_{\odot}$. It is shown that neutrinos are likely to beemitted primarily toward the outward direction in the vicinity of therotational axis and their energy density may be high enough to launch alow-energy short gamma-ray burst via the neutrino-antineutrinopair-annihilation process with the total energy deposition $\sim10^{47}$--$10^{49}$ ergs. It is also shown in our model that for $M_{\rmBH}=3M_{\odot}$, the neutrino luminosity is larger than the electromagneticluminosity while for $M_{\rm BH}=6M_{\odot}$, the neutrino luminosity iscomparable to or slightly smaller than the electromagnetic luminosity.

Radiation Magnetohydrodynamics for Black Hole-Torus System in Full General Relativity: A Step toward Physical Simulation