Accoppiamento tra le soluzioni alle equazioni di Einstein di buco nero e quelle cosmologiche

In general relativity black holes are described as vacuum axisymmetric solutions to Einstein's equations. Since they are vacuum solutions, they tend to flat Minkowski spacetime at spatial infinity. The presently accepted relativistic cosmological model, however, is a Robertson-Walker metric that is only spatially flat and, in particular, the universe expands, isotropically and homogeneously. This thesis investigates McVittie's generalization of the simplest, non-rotating, static black hole, described by the Schwarzschild solution to Einstein's equation. This new solution correctly tends to the Robertson-Walker cosmological solution at spatial infinity. The main difference between this generalization and the original Schwarzschild black hole is that its mass is not constant in time anymore and is, in fact, coupled with the cosmological scale factor. In particular the mass of a McVittie black hole grows as the universe expands and this effect exactly compensates the corresponding rarefaction of a spatially homogeneous distribution of black holes. The balance between these two effects can be seen as one possible origin of the cosmological constant seen as a component of the energy density that does not depends on the scale factor of the universe. Recent observations show some agreement between the measured mass of black holes, cosmological constant and the McVittie predicition.