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We perform a numerical free evolution of a selfgravitating, sphericallysymmetric scalar field satisfying the wave equation. The evolution equationscan be written in a very simple form and are symmetric hyperbolic inEddington-Finkelstein coordinates. The simplicity of the system allow todisplay and deal with the typical gauge instability present in thesecoordinates. The numerical evolution is performed with a standard method oflines fourth order in space and time. The time algorithm is Runge-Kutta whilethe space discrete derivative is symmetric (non-dissipative). The constraintsare preserved under evolution (within numerical errors) and we are able toreproduce several known results.Comment: 15 pages, 15 figure

Free evolution of self-gravitating, spherically symmetric waves