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The extended conformal Einstein field equations with matter: the Einstein-Maxwell field. (English) Zbl 1239.53018
Summary: A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. The resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know a priori the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain (i) a new proof of the stability of Einstein-Maxwell de Sitter-like space-times; (ii) a proof of the semi-global stability of purely radiative Einstein-Maxwell space-times.

MSC:
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
83C22 Einstein-Maxwell equations
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