242 research outputs found
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
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
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
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
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 ) 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
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
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
On the uniqueness of smooth, stationary black holes in vacuum
We prove a conditional "no hair" theorem for smooth manifolds: if is the
domain of outer communication of a smooth, regular, stationary Einstein vacuum,
and if a technical condition relating the Ernst potential and Killing scalar is
satisfied on the bifurcate sphere, then is locally isometric to the domain
of outer communication of a Kerr space-time.Comment: Various correction
Einstein-Maxwell gravitational instantons and five dimensional solitonic strings
We study various aspects of four dimensional Einstein-Maxwell multicentred
gravitational instantons. These are half-BPS Riemannian backgrounds of minimal
N=2 supergravity, asymptotic to R^4, R^3 x S^1 or AdS_2 x S^2. Unlike for the
Gibbons-Hawking solutions, the topology is not restricted by boundary
conditions. We discuss the classical metric on the instanton moduli space. One
class of these solutions may be lifted to causal and regular multi `solitonic
strings', without horizons, of 4+1 dimensional N=2 supergravity, carrying null
momentum.Comment: 1+30 page
Adaptive Event Horizon Tracking and Critical Phenomena in Binary Black Hole Coalescence
This work establishes critical phenomena in the topological transition of
black hole coalescence. We describe and validate a computational front tracking
event horizon solver, developed for generic studies of the black hole
coalescence problem. We then apply this to the Kastor - Traschen axisymmetric
analytic solution of the extremal Maxwell - Einstein black hole merger with
cosmological constant. The surprising result of this computational analysis is
a power law scaling of the minimal throat proportional to time. The minimal
throat connecting the two holes obeys this power law during a short time
immediately at the beginning of merger. We also confirm the behavior
analytically. Thus, at least in one axisymmetric situation a critical
phenomenon exists. We give arguments for a broader universality class than the
restricted requirements of the Kastor - Traschen solution.Comment: 13 pages, 20 figures Corrected labels on figures 17 through 20.
Corrected typos in references. Added some comment
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