In this paper we study the global initial value problem for the spherically symmetric Einstein-scalar field equations in the large. We introduce the concept of a generalized solution of our problem, and, taking as initial hypersurface a future light cone with vertex at the center of symmetry, we prove, without any restriction on the size of the initial data, the global, in retarded time, existence of generalized solutions.
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Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. ReferencesChristodoulou, D.: The problem of a self-gravitating scalar field. Commun. Math. Phys.105, 337–361 (1986)
Leray, J.: Sur le mouvement d'un liquide visquex emplissant l'espace. Acta Math.63, 193–248 (1934)
Departments of Mathematics and Physics, Syracuse University, Syracuse, New York, USA
Demetrios Christodoulou
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
About this article Cite this articleChristodoulou, D. Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large. Commun.Math. Phys. 106, 587–621 (1986). https://doi.org/10.1007/BF01463398
Received: 09 November 1984
Revised: 16 June 1986
Issue Date: December 1986
DOI: https://doi.org/10.1007/BF01463398
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