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Conformal wave equations for the Einstein-tracefree matter system. (arXiv:1902.01816v1 [gr-qc])
来源于:arXiv
Inspired by a similar analysis for the vacuum conformal Einstein field
equations by Paetz [Ann. H. Poincar\'e 16, 2059 (2015)], in this article we
show how to construct a system of quasilinear wave equations for the geometric
fields associated to the conformal Einstein field equations coupled to matter
models whose energy-momentum tensor has vanishing trace. In this case, the
equation of conservation for the energy-momentum tensor is conformally
invariant. Our analysis includes the construction of a subsidiary evolution
system which allows to prove the propagation of the constraints. We discuss how
the underlying structure behind these systems of equations is the integrability
conditions satisfied by the conformal field equations. The main result of our
analysis is that both the evolution and subsidiary equations for the geometric
part of the conformal Einstein-tracefree matter field equations close without
the need of any further assumption on the matter models other than the
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