Bounded variation solutions of the spherically symmetric Einstein-scalar field equations. (English) Zbl 0853.35122

Christodoulou, Demetrios

Commun. Pure Appl. Math. 46, No. 8, 1131-1220 (1993).

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

Keywords:

spherically symmetric solutions of bounded variation; Einstein equations

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.