Gravitons and black holes in loop quantum gravity.

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In the first part of the talk we introduce a technique to compute large scale correlations in LQG and spinfoam models. Using this formalism we calculate some components of the graviton propagator and of the n-points function.
In the second part we apply the ideas suggested by LQG to the black hole interior . The result of the quantum analysis is that the classical singularity disappears in loop quantum gravity. Solving the semiclassical Einstein equation of motion we obtain a metric regular and singularity free in contrast to the classical one. By using the new metric we calculate the Hawking temperature, entropy and we study the mass evaporation process.