  It is shown that by making use of the Kodama vector field, as a preferred
time evolution vector field, in spherically symmetric dynamical systems
unexpected simplifications arise. In particular, the evolution equations
relevant for the case of a massless scalar field minimally coupled to gravity
are investigated. The simplest form of these equations in the 'canonical gauge'
are known to possess the character of a mixed first order elliptic-hyperbolic
system. The advantages related to the use of the Kodama vector field are
two-folded although they show up simultaneously. First, it is found that the
true degrees of freedom separate. Second, a subset of the field equations
possessing the form of a first order symmetric hyperbolic system for these
preferred degrees of freedom is singled out. It is also demonstrated, in the
appendix, that the above results generalise straightforwardly to the case of a
generic self-interacting scalar field.
