Black hole evaporation within a momentum-dependent metric

Abstract

We investigate the black hole thermodynamics in a "deformed" relativity framework where the energy-momentum dispersion law is Lorentz-violating and the Schwarzchild-like metric is momentum-dependent with a Planckian cut-off. We obtain net deviations of the basic thermodynamical quantities from the Hawking-Bekenstein predictions: actually, the black hole evaporation is expected to quit at a nonzero critical mass value (of the order of the Planck mass), leaving a zero temperature remnant, and avoiding a spacetime singularity. Quite surprisingly, the present semiclassical corrections to black hole temperature, entropy, and heat capacity turn out to be identical to the ones obtained within some quantum approaches.