Thermodynamics and luminosities of rainbow black holes

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. As result of the nonlinearity of the Lorentz transformation, the energy-momentum dispersion relation is modified. One simple way to import DSR to curved spacetime is "Gravity's rainbow", where the spacetime background felt by a test particle would depend on its energy. Focusing on the "Amelino-Camelia dispersion relation" which is E-2 = m(2) + p(2) [1 - eta (E/m(p))(n)] with n > 0, we investigate the thermodynamical properties of a Schwarzschild black hole and a static uncharged black string for all possible values of fri and n in the framework of rainbow gravity. It shows that there are non-vanishing minimum masses for these two black holes in the cases with n < 0 and n >= 2. Considering effects of rainbow gravity on both the Hawking temperature and radius of the event horizon, we use the geometric optics approximation to compute luminosities of a 2D black hole, a Schwarzschild one and a static uncharged black string. It is found that the luminosities can be significantly suppressed or boosted depending on the values of n and n.