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


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
Full Text: DOI


[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.