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On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations. (English) Zbl 0737.53070
Up to the present times, some skillful reformulations of Einstein’s field equations lead to new insights. The better part of the reviewed paper is such a reformulation, where gravitation is coupled with a Yang-Mills field to a compact Lie group. None of the applied procedures (i) introduction of a conformal factor into Einstein’s equations, (ii) Penrose’s conformal compactification, (iii) harmonic coordinates and Lorentz gauge, (iv) translation into spinor notation, (v) Kato’s theory of symmetric hyperbolic systems, is new by itself but their consistent combination produced results which motivated a geometrical journal to publish this mainly analytical paper of unusual length. The field equations behave rather well near the conformal boundary and can be conveniently studied there. Moreover, Kato’s theory provides global solutions, admittedly with a prescribed simple spacetime topology. There is stability in the sense that known solutions, like De Sitter spacetime, can be perturbed in order to produce more solutions.

53Z05 Applications of differential geometry to physics
35Q75 PDEs in connection with relativity and gravitational theory
53C80 Applications of global differential geometry to the sciences
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