21,583 research outputs found
The time evolution of marginally trapped surfaces
In previous work we have shown the existence of a dynamical horizon or
marginally trapped tube (MOTT) containing a given strictly stable marginally
outer trapped surface (MOTS). In this paper we show some results on the global
behavior of MOTTs assuming the null energy condition. In particular we show
that MOTSs persist in the sense that every Cauchy surface in the future of a
given Cauchy surface containing a MOTS also must contain a MOTS. We describe a
situation where the evolving outermost MOTS must jump during the coalescence of
two seperate MOTSs. We furthermore characterize the behavior of MOTSs in the
case that the principal eigenvalue vanishes under a genericity assumption. This
leads to a regularity result for the tube of outermost MOTSs under the
genericity assumption. This tube is then smooth up to finitely many jump times.
Finally we discuss the relation of MOTSs to singularities of a space-time.Comment: 21 pages. This revision corrects some typos and contains more
detailed proofs than the original versio
The fifth most prevalent disease is being neglected by public health organisations
The progress towards reduction of global mortality has produced an epidemiological transition towards non-fatal diseases, which challenge the ability of the world’s population to live in full health. Although traumatic dental injuries are not lethal, their treatment is more expensive (US$2 000 000–5 000 000 per million inhabitants) and time-consuming than that of all the other bodily injuries, making dental rehabilitation less likely among disadvantaged individuals. Since untreated traumatic dental injuries have a negative social, functional, and emotional effect in children and adolescents, differences in treatment of these injuries between children from different countries and social classes produce disparities in their quality of life
String Effects on Fermi--Dirac Correlation Measurements
We investigate some recent measurements of Fermi--Dirac correlations by the
LEP collaborations indicating surprisingly small source radii for the
production of baryons in -annihilation at the peak. In the
hadronization models there are besides the Fermi--Dirac correlation effect also
a strong dynamical (anti-)correlation. We demonstrate that the extraction of
the pure FD effect is highly dependent on a realistic Monte Carlo event
generator, both for separation of those dynamical correlations which are not
related to Fermi--Dirac statistics, and for corrections of the data and
background subtractions. Although the model can be tuned to well reproduce
single particle distributions, there are large model-uncertainties when it
comes to correlations between identical baryons. We therefore, unfortunately,
have to conclude that it is at present not possible to make any firm conclusion
about the source radii relevant for baryon production at LEP
Bounds on area and charge for marginally trapped surfaces with cosmological constant
We sharpen the known inequalities and between the area and the electric charge of a stable marginally
outer trapped surface (MOTS) of genus g in the presence of a cosmological
constant . In particular, instead of requiring stability we include
the principal eigenvalue of the stability operator. For we obtain a lower and an upper bound for in terms of as well as the upper bound for the charge, which reduces to in the stable case . For
there remains only a lower bound on . In the spherically symmetric, static,
stable case one of the area inequalities is saturated iff the surface gravity
vanishes. We also discuss implications of our inequalities for "jumps" and
mergers of charged MOTS.Comment: minor corrections to previous version and to published versio
The Cosmological Time Function
Let be a time oriented Lorentzian manifold and the Lorentzian
distance on . The function is the cosmological
time function of , where as usual means that is in the causal
past of . This function is called regular iff for all
and also along every past inextendible causal curve. If the
cosmological time function of a space time is regular it has
several pleasant consequences: (1) It forces to be globally hyperbolic,
(2) every point of can be connected to the initial singularity by a
rest curve (i.e., a timelike geodesic ray that maximizes the distance to the
singularity), (3) the function is a time function in the usual sense, in
particular (4) is continuous, in fact locally Lipschitz and the second
derivatives of exist almost everywhere.Comment: 19 pages, AEI preprint, latex2e with amsmath and amsth
r-modes in Relativistic Superfluid Stars
We discuss the modal properties of the -modes of relativistic superfluid
neutron stars, taking account of the entrainment effects between superfluids.
In this paper, the neutron stars are assumed to be filled with neutron and
proton superfluids and the strength of the entrainment effects between the
superfluids are represented by a single parameter . We find that the
basic properties of the -modes in a relativistic superfluid star are very
similar to those found for a Newtonian superfluid star. The -modes of a
relativistic superfluid star are split into two families, ordinary fluid-like
-modes (-mode) and superfluid-like -modes (-mode). The two
superfluids counter-move for the -modes, while they co-move for the
-modes. For the -modes, the quantity is
almost independent of the entrainment parameter , where and
are the azimuthal wave number and the oscillation frequency observed by an
inertial observer at spatial infinity, respectively. For the -modes, on
the other hand, almost linearly increases with increasing . It
is also found that the radiation driven instability due to the -modes is
much weaker than that of the -modes because the matter current associated
with the axial parity perturbations almost completely vanishes.Comment: 14 pages, 4 figures. To appear in Physical Review
Relativistic Two-stream Instability
We study the (local) propagation of plane waves in a relativistic,
non-dissipative, two-fluid system, allowing for a relative velocity in the
"background" configuration. The main aim is to analyze relativistic two-stream
instability. This instability requires a relative flow -- either across an
interface or when two or more fluids interpenetrate -- and can be triggered,
for example, when one-dimensional plane-waves appear to be left-moving with
respect to one fluid, but right-moving with respect to another. The dispersion
relation of the two-fluid system is studied for different two-fluid equations
of state: (i) the "free" (where there is no direct coupling between the fluid
densities), (ii) coupled, and (iii) entrained (where the fluid momenta are
linear combinations of the velocities) cases are considered in a
frame-independent fashion (eg. no restriction to the rest-frame of either
fluid). As a by-product of our analysis we determine the necessary conditions
for a two-fluid system to be causal and absolutely stable and establish a new
constraint on the entrainment.Comment: 15 pages, 2 eps-figure
Gravitational Instantons and special geometry
The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on , that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. In this paper we show that the Chen-Teo instanton is Hermitian and non-K\"ahler. It follows that all known examples of gravitational instantons are Hermitian
A parabolic free boundary problem with Bernoulli type condition on the free boundary
Consider the parabolic free boundary problem For a
realistic class of solutions, containing for example {\em all} limits of the
singular perturbation problem we prove that one-sided
flatness of the free boundary implies regularity.
In particular, we show that the topological free boundary
can be decomposed into an {\em open} regular set (relative to
) which is locally a surface with H\"older-continuous space
normal, and a closed singular set.
Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli
(1981) to more general solutions as well as the time-dependent case. Our proof
uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace
the core of that paper, which relies on non-positive mean curvature at singular
points, by an argument based on scaling discrepancies, which promises to be
applicable to more general free boundary or free discontinuity problems
The rotational modes of relativistic stars: Numerical results
We study the inertial modes of slowly rotating, fully relativistic compact
stars. The equations that govern perturbations of both barotropic and
non-barotropic models are discussed, but we present numerical results only for
the barotropic case. For barotropic stars all inertial modes are a hybrid
mixture of axial and polar perturbations. We use a spectral method to solve for
such modes of various polytropic models. Our main attention is on modes that
can be driven unstable by the emission of gravitational waves. Hence, we
calculate the gravitational-wave growth timescale for these unstable modes and
compare the results to previous estimates obtained in Newtonian gravity (i.e.
using post-Newtonian radiation formulas). We find that the inertial modes are
slightly stabilized by relativistic effects, but that previous conclusions
concerning eg. the unstable r-modes remain essentially unaltered when the
problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure
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