Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations. (English) Zbl 1055.83002

Dafermos, Mihalis

Ann. Math. (2) 158, No. 3, 875-928 (2003).

Author’s abstract: This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar field equations. For an open set of initial data whose closure contains in particular Reissner-Nordström data, the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose.

Reviewer: Giovanni Giachetta (Camerino)

MSC:

83C05	Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C22	Einstein-Maxwell equations
58J45	Hyperbolic equations on manifolds
83C75	Space-time singularities, cosmic censorship, etc.
83C57	Black holes
53Z05	Applications of differential geometry to physics

Keywords:

Einstein-Maxwell equations; Cauchy surface; black hole; cosmic censorship