2,868 research outputs found
On the classification of type D spacetimes
We give a classification of the type D spacetimes based on the invariant
differential properties of the Weyl principal structure. Our classification is
established using tensorial invariants of the Weyl tensor and, consequently,
besides its intrinsic nature, it is valid for the whole set of the type D
metrics and it applies on both, vacuum and non-vacuum solutions. We consider
the Cotton-zero type D metrics and we study the classes that are compatible
with this condition. The subfamily of spacetimes with constant argument of the
Weyl eigenvalue is analyzed in more detail by offering a canonical expression
for the metric tensor and by giving a generalization of some results about the
non-existence of purely magnetic solutions. The usefulness of these results is
illustrated in characterizing and classifying a family of Einstein-Maxwell
solutions. Our approach permits us to give intrinsic and explicit conditions
that label every metric, obtaining in this way an operational algorithm to
detect them. In particular a characterization of the Reissner-Nordstr\"{o}m
metric is accomplished.Comment: 29 pages, 0 figure
The Topology of Branching Universes
The purpose of this paper is to survey the possible topologies of branching
space-times, and, in particular, to refute the popular notion in the literature
that a branching space-time requires a non-Hausdorff topology
Probing the dynamics of quasicrystal growth using synchrotron live imaging
The dynamics of quasicrystal growth remains an unsolved problem in condensed
matter. By means of synchrotron live imaging, facetted growth proceeding by the
tangential motion of ledges at the solid-melt interface is clearly evidenced
all along the solidification of icosahedral AlPdMn quasicrystals. The effect of
interface kinetics is significant so that nucleation and free growth of new
facetted grains occur in the melt when the solidification rate is increased.
The evolution of these grains is explained in details, which reveals the
crucial role of aluminum rejection, both in the poisoning of grain growth and
driving fluid flow
Cohomological tautness for Riemannian foliations
In this paper we present some new results on the tautness of Riemannian
foliations in their historical context. The first part of the paper gives a
short history of the problem. For a closed manifold, the tautness of a
Riemannian foliation can be characterized cohomologically. We extend this
cohomological characterization to a class of foliations which includes the
foliated strata of any singular Riemannian foliation of a closed manifold
Modified differentials and basic cohomology for Riemannian foliations
We define a new version of the exterior derivative on the basic forms of a
Riemannian foliation to obtain a new form of basic cohomology that satisfies
Poincar\'e duality in the transversally orientable case. We use this twisted
basic cohomology to show relationships between curvature, tautness, and
vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad
Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method
We will present results of a numerical integration of a maximally sliced
Schwarzschild black hole using a smooth lattice method. The results show no
signs of any instability forming during the evolutions to t=1000m. The
principle features of our method are i) the use of a lattice to record the
geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM
equations to the lattice and iii) the use of the Bianchi identities to assist
in the computation of the curvatures. No other special techniques are used. The
evolution is unconstrained and the ADM equations are used in their standard
form.Comment: 47 pages including 26 figures, plain TeX, also available at
http://www.maths.monash.edu.au/~leo/preprint
Use of three-dimensional computed tomography overlay for real-time cryoballoon ablation in atrial fibrillation reduces radiation dose and contrast dye
AIMS: Cryoballoon pulmonary vein (PV) isolation in patients with atrial fibrillation has proven to be effective in short-term and long-term follow-up. To visualise the PV anatomy, pre-ablation contrast pulmonary venography is commonly performed. Three-dimensional (3D) computed tomography (CT) overlay is a new technique creating a live 3D image of the left atrium by integrating a previously obtained CT scan during fluoroscopy. To evaluate the benefits of 3D CT overlay during cryoballoon ablation, we studied the use of 3D CT overlay versus contrast pulmonary venography in a randomised fashion in patients with paroxysmal atrial fibrillation undergoing cryoballoon PV isolation. METHODS AND RESULTS: Between October 2012 and June 2013, 30 patients accepted for PV isolation were randomised to cryoballoon PV isolation using either 3D CT overlay or contrast pulmonary venography. All patients underwent a pre-procedural cardiac CT for evaluation of the anatomy of the left atrium (LA) and the PVs. In the 3D CT overlay group, a 3D reconstruction of the LA and PVs was made. An overlay of the CT reconstruction was then projected over live fluoroscopy. Patients in the contrast pulmonary venography group received significantly more contrast agent (77.1 ± 21.2 cc vs 40.1 ± 17.6 cc, p < 0.001) and radiation (43.0 ± 21.9 Gy.cm2 vs 28.41 ± 11.7 Gy.cm2, p = 0.04) than subjects in the 3D CT overlay group. There was no difference in total procedure time, fluoroscopy time and the amount of cryoapplications between the two groups. CONCLUSION: The use of 3D CT overlay decreases radiation and contrast dye exposure and can assist in guiding cryoballoon-based PV isolation
Late time behaviour of the maximal slicing of the Schwarzschild black hole
A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be
evolved into a foliation of the -region of the spacetime by maximal
surfaces with the requirement that time runs equally fast at both spatial ends
of the manifold. This paper studies the behaviour of these slices in the limit
as proper time-at-infinity becomes arbitrarily large and gives an analytic
expression for the collapse of the lapse.Comment: 18 pages, Latex, no figure
Topology Change and Causal Continuity
The result that, for a scalar quantum field propagating on a ``trousers''
topology in 1+1 dimensions, the crotch singularity is a source for an infinite
burst of energy has been used to argue against the occurrence of topology
change in quantum gravity. We draw attention to a conjecture due to Sorkin that
it may be the particular type of topology change involved in the trousers
transition that is problematic and that other topology changes may not cause
the same difficulties. The conjecture links the singular behaviour to the
existence of ``causal discontinuities'' in the spacetime and relies on a
classification of topology changes using Morse theory. We investigate various
topology changing transitions, including the pair production of black holes and
of topological geons, in the light of these ideas.Comment: Latex, 28 pages, 10 figures, small changes in text (one figure
removed), conclusions remain unchanged. Accepted for publication in Physical
Review
Vacuum Spacetimes with Future Trapped Surfaces
In this article we show that one can construct initial data for the Einstein
equations which satisfy the vacuum constraints. This initial data is defined on
a manifold with topology with a regular center and is asymptotically
flat. Further, this initial data will contain an annular region which is
foliated by two-surfaces of topology . These two-surfaces are future
trapped in the language of Penrose. The Penrose singularity theorem guarantees
that the vacuum spacetime which evolves from this initial data is future null
incomplete.Comment: 19 page
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