  Our contribution concerns with the numerical solution of the 3D general
relativistic hydrodynamical system of equations within the framework of the 3+1
formalism. We summarize the theoretical ingredients which are necessary in
order to build up a numerical scheme based on the solution of local Riemann
problems. Hence, the full spectral decomposition of the Jacobian matrices of
the system, i.e., the eigenvalues and the right and left eigenvectors, is
explicitly shown. An alternative approach consists in using any of the special
relativistic Riemann solvers recently developed for describing the evolution of
special relativistic flows. Our proposal relies on a local change of
coordinates in terms of which the spacetime metric is locally Minkowskian and
permits an accurate description of numerical general relativistic
hydrodynamics.
