The study of the ADM formalism for the General Relativity Theory through the foliation methods on the Cauchy surfacesis is realized. The mathematical development that leads to the Hamiltonian formulation of General Relativity is presented explicitly.

Se evalúa la distribucion de energía de los agujeros negros de Schwarzschild, Reissner-Nordström y Kerr-Newman usando el complejo energía-momento de Møller. Notamos que la expresión de Møller es más general que los pseudotensores de Eisntein, Landau-Lifshitz y Weinberg, ya que la energía puede ser calculada usando directamente las coordinadas esféricas sin la necesidad de transformación a las coordinadas cartesianas.

We analyse the process of gravitational collapse using Press-Schechter theory in order to predict the existence of Primordial Black Holes, PBHs, using the Josan’s restriction and the latest cosmological parameters measured by Planck satellite. Assuming a gaussian fluctuation on the perturbation in the early Universe, we find that PBHs with mass M > 1012 kg, have not evaporated yet. Comparing with the mass fraction PBH = 10−20 and assuming that the PBHs energy density should not exceed the Cold Dark Matter, CDM, energy density, we constraint the spectral index (blue espectra) to ns < 1.4 and obtain a value of the power spectrum P ≈ 10−2.