  Since Stephen Hawking discovered that black holes emit thermal radiation,
black holes have become the theoretical laboratories for testing our ideas on
quantum gravity. This dissertation is devoted to the study of singularities,
the formation of black holes by gravitational collapse and the global structure
of spacetime. All our investigations are in the context of a recently proposed
approach to quantum gravity, which breaks Lorentz and diffeomorphism symmetries
at very high energies.
