Quantization of the Schwarzschild black hole: a Noether symmetry
  approach
  We study the canonical formalism of a spherically symmetric space-time. In
the context of the 3+1 decomposition with respect to the radial coordinate $r$,
we set up an effective Lagrangian in which a couple of metric functions play
the role of independent variables. We show that the resulting $r$-Hamiltonian
yields the correct classical solutions which can be identified with the
Schwarzschild black hole. The Noether symmetry of model is then investigated by
utilizing the behavior of the corresponding Lagrangian under the infinitesimal
generators of the desired symmetry. According to the Noether symmetry approach,
we also quantize the model and show that the existence of a Noether symmetry
yields a general solution to the Wheeler-DeWitt equation where exhibits a good
correlation with the classical regime. We use the resulting wave function in
order to (qualitative) investigate the possibility of the avoidance of
classical singularities.
