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Communications in Mathematical Physics

, Volume 109, Issue 4, pp 613–647 | Cite as

A mathematical theory of gravitational collapse

  • Demetrios Christodoulou
Article

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 massM1 is different from zero, asu → ∞, a black hole forms of massM1 surrounded by vacuum. We find the rate of decay of the metric functions and the behaviour of the scalar field on the horizon.

Keywords

Neural Network Black Hole Statistical Physic Complex System Asymptotic Behaviour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Christodoulou, D.: The problem of a self-gravitating scalar field. Commun. Math. Phys.105, 337 (1986)Google Scholar
  2. 2.
    Christodoulou, D.: Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large. Commun. Math. Phys.106, 587 (1986)Google Scholar
  3. 3.
    Christodoulou, D.: The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations. Commun. Math. Phys.109, 591 (1987)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Demetrios Christodoulou
    • 1
  1. 1.Departments of Mathematics and PhysicsSyracuse UniversitySyracuseUSA

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