×

The formation of black holes and singularities in spherically symmetric gravitational collapse. (English) Zbl 0728.53061

The author studies spherically symmetric solutions of Einstein’s equation for a massless scalar field. He shows that (M,g) contains a curvature singularity (\(| Riem|\) diverges faster than \(r^{-3})\), provided that the following mass estimate holds: Let \(C^+_ 0\) be a future directed light cone with vertex at the central geodesic. Suppose there exist spheres \(S_{1,0},S_{2,0}\subset C^+_ 0\) \((S_{2,0}\) to the future of \(S_{1,0})\) which are orthogonal to the null geodesic generators of \(C^+_ 0\) such that the (Hawking) mass function m (that coincides with the usual mass function for spherically symmetric spacetimes) satisfies \[ 2(m(S_{2,0})-m(S_{1,0})/r_{2,0}\geq E(r_{2,0}/r_{1,0})-1), \] where \(r_{i,0}\) denotes the radius of \(S_{i,0}\) and E is a certain explicitly given increasing function with \(E(0)=0\). Then (M,g) contains a singularity. But the author gives a far more detailed account of what is happening.
Reviewer: M.Kriele (Berlin)

MSC:

53C80 Applications of global differential geometry to the sciences
83C75 Space-time singularities, cosmic censorship, etc.
83C57 Black holes
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Christodoulou, Commun. Math. Phys. 105 pp 337– (1986)
[2] Christodoulou, Commun. Math. Phys. 106 pp 587– (1986)
[3] Christodoulou, Commun. Math. Phys. 109 pp 591– (1987)
[4] Christodoulou, Commun. Math. Phys. 109 pp 613– (1987)
[5] and , The global nonlinear stability of Minkowski space, to appear.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.