Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Christodoulou, 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)
Author information
Authors and Affiliations
Additional information
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
Rights and permissions
About this article
Cite this article
Christodoulou, 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:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01463398