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The problem of a self-gravitating scalar field

In this paper we begin the study of the global initial value problem for Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We reduce the problem to a single nonlinear evolution equation. Taking as initial hypersurface a future light cone with vertex at the center of symmetry, we prove, the local, in retarded time, existence and global uniqueness of classical solutions. We also prove that if the initial data is sufficiently small there exists a global classical solution which disperses in the infinite future.

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1. Department of Mathematics and Physics, Syracuse University, Syracuse, New York, USA

   Demetrios Christodoulou

1. 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

Christodoulou, D. The problem of a self-gravitating scalar field. Commun.Math. Phys. 105, 337–361 (1986). https://doi.org/10.1007/BF01205930

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• Received: 09 November 1984

• Revised: 18 December 1985

• Issue Date: September 1986

• DOI: https://doi.org/10.1007/BF01205930

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