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We present a set of four three-dimensional, general relativistic, radiationMHD simulations of black hole accretion at super-critical mass accretion rates,$\dot{M} > \dot{M}_{\rm Edd}$. We use these simulations to study how diskproperties are modified when we vary the black hole mass, the black hole spin,or the mass accretion rate. In the case of a non-rotating black hole, we findthat the total efficiency is of order $3\%\dot M c^2$, approximately a factorof two less than the efficiency of a standard thin accretion disk. Theradiation flux in the funnel along the axis is highly super-Eddington, but onlya small fraction of the energy released by accretion escapes in this region.The bulk of the $3\%\dot M c^2$ of energy emerges farther out in the disk,either in the form of photospheric emission or as a wind. In the case of ablack hole with a spin parameter of 0.7, we find a larger efficiency of about$8\%\dot M c^2$. By comparing the relative importance of advective anddiffusive radiation transport, we show that photon trapping is effective nearthe equatorial plane. However, near the disk surface, vertical transport ofradiation by diffusion dominates. We compare the properties of our fiducialthree-dimensional run with those of an equivalent two-dimensional axisymmetricmodel with a mean-field dynamo. The latter simulation runs nearly 100 timesfaster than the three-dimensional simulation, and gives very similar resultsfor time-averaged properties of the accretion flow.

Three-dimensional simulations of super-critical black hole accretion disks --- luminosities, photon trapping and variability