Hawking, Fiducial, and Free-fall Temperatures of Black Hole on Gravity's Rainbow
arXiv:1509.06846 · doi:10.1140/epjc/s10052-016-4025-9
Abstract
On gravity's rainbow, the energy of particles affects the geometry of black hole in such a way that the Hawking temperature of black hole is appropriately modified. It means that the fiducial and free-fall temperatures on the background of black hole should also be modified according to deformation of the geometry. We find that the fiducial temperature takes the blue-shifted modified Hawking temperature so that it is divergent at the horizon, while the free-fall temperature defined by employing the thermodynamic Stefan-Boltzmann relation on gravity's rainbow is finite everywhere without the blue-shift effect; in particular, it is vanishing at the horizon. In this respect, the behaviors of the two-different temperatures at the horizon show that black hole complementarity is still required on gravity's rainbow.
16 pages, 4 figures, version to appear in EPJC
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