All electro--vacuum Majumdar--Papapetrou space--times with nonsingular black holes

We show that all Majumdar--Papapetrou electrovacuum space--times with a non--empty black hole region and with a non--singular domain of outer communications are the standard Majumdar--Papapetrou space--times.Comment: 9 pages, Late

Outer trapped surfaces are dense near MOTSs

We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data containing marginally outer trapped surfaces lead to geodesically incomplete spacetimes.Comment: 14 pages, minor rewording

The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior

We prove non-existence of static, vacuum, appropriately regular, asymptotically flat black hole space-times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space-times, showing that the domains of outer communication of the Schwarzschild black holes exhaust the space of appropriately regular black hole exteriors.Comment: This version includes an addendum with a corrected proof of non-existence of zeros of the Killing vector at degenerate horizons. A problem with yet another Lemma is pointed out; this problem does not arise if one assumes analyticity of the metric. An alternative solution, that does not require analyticity, has been given in arXiv:1004.0513 [gr-qc] under appropriate global condition

On the topology of stationary black holes

We prove that the domain of outer communication of a stationary, globally hyperbolic spacetime satisfying the null energy condition must be simply connected. Under suitable additional hypotheses, this implies, in particular, that each connected component of a cross-section of the event horizon of a stationary black hole must have spherical topology.Comment: 7 pages, Late

Towards a classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior

We show that static electro-vacuum black hole space-times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon do not exist, under the supplementary hypothesis that all degenerate components of the event horizon have charges of the same sign. This extends previous uniqueness theorems of Simon and Masood-ul-Alam (where only non-degenerate horizons were allowed) and Heusler (where only degenerate horizons were allowed).Comment: Reverted to original v1; v2 was a result of a manipulation error, and was meant to be an update to gr-qc/9809088. The problems adressed in the addendum in v2 of gr-qc/9809088 apply also to this paper, and are similarly taken care of by the addendum to gr-qc/9809088, and by the analysis in arXiv:1004.0513 [gr-qc

On completeness of orbits of Killing vector fields

A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown that all Killing orbits are complete in maximal developements of asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact manifold. This result gives a significant strengthening of the uniqueness theorems for black holes.Comment: 16 pages, Latex, preprint NSF-ITP-93-4

Gravitational waves in general relativity: XIV. Bondi expansions and the ``polyhomogeneity'' of \Scri

The structure of polyhomogeneous space-times (i.e., space-times with metrics which admit an expansion in terms of $r^{-j}\log^i r$) constructed by a Bondi--Sachs type method is analysed. The occurrence of some log terms in an asymptotic expansion of the metric is related to the non--vanishing of the Weyl tensor at Scri. Various quantities of interest, including the Bondi mass loss formula, the peeling--off of the Riemann tensor and the Newman--Penrose constants of motion are re-examined in this context.Comment: LaTeX, 28pp, CMA-MR14-9

The Trautman-Bondi mass of hyperboloidal initial data sets

We give a definition of mass for conformally compactifiable initial data sets. The asymptotic conditions are compatible with existence of gravitational radiation, and the compactifications are allowed to be polyhomogeneous. We show that the resulting mass is a geometric invariant, and we prove positivity thereof in the case of a spherical conformal infinity. When R(g) - or, equivalently, the trace of the extrinsic curvature tensor - tends to a negative constant to order one at infinity, the definition is expressed purely in terms of three-dimensional or two-dimensional objects