Bounded variation solutions of the spherically symmetric Einstein-scalar field equations. (English) Zbl 0853.35122
The author gives a self-contained, comprehensive account of the spherically symmetric solutions of bounded variation of the Einstein equations
\[
R_{\mu\nu}- \textstyle{{1\over 2}} g_{\mu\nu} R= 2T_{\mu\nu},
\]
where the energy tensor \(T_{\mu\nu}\) is that of a scalar field \(\phi\), so that,
\[
T_{\mu\nu}= \partial_\mu \phi \partial_\nu \phi- \textstyle{{1\over 2}} g_{\mu\nu} \partial^\alpha \phi \partial_\alpha \phi.
\]
Reviewer: A.D.Osborne (Keele)
MSC:
| 35Q75 | PDEs in connection with relativity and gravitational theory |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
| 53Z05 | Applications of differential geometry to physics |
References:
| [1] | Christodoulou, Comm. Pure Appl. Math. 44 pp 339– (1991) |
| [2] | Christodoulou, Comm. Math. Phys. 109 pp 613– (1987) |
| [3] | Chandrasekhar, Proc. Roy. Soc. London A 398 pp 223– (1985) |
| [4] | Geometric Measure Theory, Springer-Verlag, New York, 1969. |
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