On periodic solutions of nonlinear wave equations, including Einstein equations with a negative cosmological constant

We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions of the vacuum, or of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$ equations, with a negative cosmological constant.Comment: 15 pages, 1 figur

On rigidity of analytic black holes

We establish global extendibility (to the domain of outer communications) of locally defined isometries of appropriately regular analytic black holes. This allows us to fill a gap in the Hawking-Ellis proof of black-hole rigidity.Comment: 10 pages, latex with amssym

Stationary Black Holes

We review the theory of stationary black hole solutions of vacuum Einstein equations.Comment: 10 pages, 2 figures, to appear in Encyclopedia of Mathematical Physics in 200

KIDs like cones

We analyze vacuum Killing Initial Data on characteristic Cauchy surfaces. A general theorem on existence of Killing vectors in the domain of dependence is proved, and some special cases are analyzed in detail, including the case of bifurcate Killing horizons.Comment: 32 pages; improvement of theorem 1.2; short appendix on Fuchsian ODEs added; section 3.3 and an appendix related to it added, which give a useful application of our analysis to bifurcate horizon

Strong cosmic censorship in vacuum space--times with compact, locally homogeneous Cauchy surfaces

We consider the question of strong cosmic censorship in spatially compact, spatially locally homogeneous vacuum models. We show in particular that strong cosmic censorship holds in Bianchi IX vacuum space--times with spherical spatial topology.Comment: Latex, 38 page