We prove that Maxwell fields of asymptotically flat solutions of the Einstein-Maxwell equations inherit the stationarity of the metric.
We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.
We construct a Kruskal-Szekeres-type analytic extension of the Emparan-Reall black ring, and investigate its geometry. We prove that the extension is maximal, globally hyperbolic, and unique within a natural class of extensions. The key to those resu
lts is the proof that causal geodesics are either complete, or approach a singular boundary in finite affine time. Alternative maximal analytic extensions are also constructed.
The standard topological censorship theorems require asymptotic hypotheses which are too restrictive for several situations of interest. In this paper we prove a version of topological censorship under significantly weaker conditions, compatible e.g.
with solutions with Kaluza-Klein asymptotic behavior. In particular we prove simple connectedness of the quotient of the domain of outer communications by the group of symmetries for models which are asymptotically flat, or asymptotically anti-de Sitter, in a Kaluza-Klein sense. This allows one, e.g., to define the twist potentials needed for the reduction of the field equations in uniqueness theorems. Finally, the methods used to prove the above are used to show that weakly trapped compact surfaces cannot be seen from Scri.
We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions $nge 3$, or fast decay conditions in $nge 5$, or a genericity condition in $nge 9$, can be deformed, by a deformation which is supported arbitrarily far
in the asymptotic region, to ones which are exactly Kottler (Schwarzschild- adS) in the asymptotic region.
We consider (n+1)--dimensional, stationary, asymptotically flat, or Kaluza-Klein asymptotically flat black holes, with an abelian $s$--dimensional subgroup of the isometry group satisfying an orthogonal integrability condition. Under suitable regular
ity conditions we prove that the area of the group orbits is positive on the domain of outer communications, vanishing only on its boundary and on the symmetry axis. We further show that the orbits of the connected component of the isometry group are timelike throughout the domain of outer communications. Those results provide a starting point for the classification of such black holes. Finally, we show non-existence of zeros of static Killing vectors on degenerate Killing horizons, as needed for the generalisation of the static no-hair theorem to higher dimensions.
Following an argument proposed by Mason, we prove that there are no algebraically special asymptotically simple vacuum space-times with a smooth, shear-free, geodesic congruence of principal null directions extending transversally to a cross-section
of Scri. Our analysis leaves the door open for escaping this conclusion if the congruence is not smooth, or not transverse to Scri. One of the elements of the proof is a new rigidity theorem for the Trautman-Bondi mass.
We extend the validity of Dains angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are invariant under a U(1) action and which admit a twist potential.
We extend the validity of Brills axisymmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.
We prove an inequality relating the trace of the extrinsic curvature, the total angular momentum, the centre of mass, and the Trautman-Bondi mass for a class of gravitational initial data sets with constant mean curvature extending to null infinity.
As an application we obtain non-existence results for the asymptotic Dirichlet problem for CMC hypersurfaces in stationary space-times.
