Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-11-10
Class.Quant.Grav. 23 (2006) 115-124
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
9 pages, to appear in Class. Quant. Grav
Scientific paper
10.1088/0264-9381/23/1/006
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.
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