Abstract
We study the asymptotic behaviour, as the retarded timeu tends to infinity, of the solutions of Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We prove that when the final Bondi massM 1 is different from zero, asu → ∞, a black hole forms of massM 1 surrounded by vacuum. We find the rate of decay of the metric functions and the behaviour of the scalar field on the horizon.
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Christodoulou, D.: The problem of a self-gravitating scalar field. Commun. Math. Phys.105, 337 (1986)
Christodoulou, D.: Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large. Commun. Math. Phys.106, 587 (1986)
Christodoulou, D.: The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations. Commun. Math. Phys.109, 591 (1987)
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Communicated by S.-T. Yau
Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University
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Christodoulou, D. A mathematical theory of gravitational collapse. Commun.Math. Phys. 109, 613–647 (1987). https://doi.org/10.1007/BF01208960
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DOI: https://doi.org/10.1007/BF01208960