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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, \[ T_{\mu\nu}= \partial_\mu \phi \partial_\nu \phi- \textstyle{{1\over 2}} g_{\mu\nu} \partial^\alpha \phi \partial_\alpha \phi. \]

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
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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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