Aspects of quantum gravity: Quantum space-time and black hole thermodynamics

This work is devoted to the study of certain quantum properties of space-time at the Planck scale and of black holes. We discuss the possibility that in quantum gravity scenarios the symmetry structure of flat space-time might deviate Bruin the classical relativistic picture and lead to broken or deformed Poincare invariance. The striking feature of these "quantum" space-time models is the possibility that they might have experimentally observable effects. We discuss how a purely kinematical model within these frameworks, besides providing the threshold anomalies needed to explain the existence of above-GZK cosmic rays, can modify the Bachall-Waxman bound on the flux of neutrinos that are expected to be produced together with such cosmic rays.; A relevant characteristic of "quantum" space-time scenarios with modifications of relativistic kinematics is the emergence of a Planck-scale particle localization limit that reflects the presence of the Planck length as an intrinsic spatial resolution limit for regimes in which quantum and gravitational effects are of the same magnitude. We propose a remarkable argument which relates the type of quantum gravity corrections to the Bekenstein-Hawking entropy-area relation for black holes and the form of the Planck-scale particle localization limit. Using this argument we are able to constraint the form of the deformed energy-momentum dispersion relation expected to emerge in the low-energy limit of loop quantum gravity. The same argument is then generalized to quantum gravity frameworks which predict a modifications of Heisenberg's uncertainty relation. We carried on a systematic study of the effects of modified energy-momentum dispersion relation and generalized uncertainty principle for an evaporating black hole obtaining also results for Planck-scale modifications of the spectrum of a radiating black-body.; Finally, we extend our study of quantum gravity corrections to the Hawking radiation spectrum by adapting the tunneling picture proposed by Parikh and Wilczek including, in such a way, non-thermal corrections due to back-reaction of the emitted particle. It is also showed that a quantum fluctuating black hole horizon, characterized by a "quantum ergosphere" produces the same type of modification to the emission spectrum expected when higher order quantum gravity corrections to the entropy-area relation are present.