103 research outputs found
Perturbative Solutions of the Extended Constraint Equations in General Relativity
The extended constraint equations arise as a special case of the conformal
constraint equations that are satisfied by an initial data hypersurface in
an asymptotically simple spacetime satisfying the vacuum conformal Einstein
equations developed by H. Friedrich. The extended constraint equations consist
of a quasi-linear system of partial differential equations for the induced
metric, the second fundamental form and two other tensorial quantities defined
on , and are equivalent to the usual constraint equations that satisfies
as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum
equation. This article develops a method for finding perturbative,
asymptotically flat solutions of the extended constraint equations in a
neighbourhood of the flat solution on Euclidean space. This method is
fundamentally different from the `classical' method of Lichnerowicz and York
that is used to solve the usual constraint equations.Comment: This third and final version has been accepted for publication in
Communications in Mathematical Physic
Spatial asymptotic expansions in the Navier-Stokes equation
We prove that the Navier-Stokes equation for a viscous incompressible fluid
in is locally well-posed in spaces of functions allowing spatial
asymptotic expansions with log terms as of any a priori given
order. The solution depends analytically on the initial data and time so that
for any it can be holomorphically extended in time to a
conic sector in with angle at zero. We discuss the
approximation of solutions by their asymptotic parts
Odd-parity perturbations of self-similar Vaidya spacetime
We carry out an analytic study of odd-parity perturbations of the
self-similar Vaidya space-times that admit a naked singularity. It is found
that an initially finite perturbation remains finite at the Cauchy horizon.
This holds not only for the gauge invariant metric and matter perturbation, but
also for all the gauge invariant perturbed Weyl curvature scalars, including
the gravitational radiation scalars. In each case, `finiteness' refers to
Sobolev norms of scalar quantities on naturally occurring spacelike
hypersurfaces, as well as pointwise values of these quantities.Comment: 28 page
General existence proof for rest frame systems in asymptotically flat space-time
We report a new result on the nice section construction used in the
definition of rest frame systems in general relativity. This construction is
needed in the study of non trivial gravitational radiating systems. We prove
existence, regularity and non-self-crossing property of solutions of the nice
section equation for general asymptotically flat space times. This proves a
conjecture enunciated in a previous work.Comment: 14 pages, no figures, LaTeX 2
Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system
We use optimal transportation techniques to show uniqueness of the compactly
supported weak solutions of the relativistic Vlasov-Darwin system. Our proof
extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to
obtain uniqueness results for the Vlasov-Poisson system.Comment: AMS-LaTeX, 21 page
(In)finite extent of stationary perfect fluids in Newtonian theory
For stationary, barotropic fluids in Newtonian gravity we give simple
criteria on the equation of state and the "law of motion" which guarantee
finite or infinite extent of the fluid region (providing a priori estimates for
the corresponding stationary Newton-Euler system). Under more restrictive
conditions, we can also exclude the presence of "hollow" configurations. Our
main result, which does not assume axial symmetry, uses the virial theorem as
the key ingredient and generalises a known result in the static case. In the
axially symmetric case stronger results are obtained and examples are
discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar
Charmonium suppression at RHIC and SPS: a hadronic baseline
A kinetic equation approach is applied to model anomalous J/psi suppression
at RHIC and SPS by absorption in a hadron resonance gas which successfully
describes statistical hadron production in both experiments. The puzzling
rapidity dependence of the PHENIX data is reproduced as a geometric effect due
to a longer absorption path for J/psi production at forward rapidity.Comment: 16 pages, 6 figures, final version accepted for publication in Phys.
Lett.
Predictions of polarized dust emission from interstellar clouds: spatial variations in the efficiency of radiative torque alignment
Polarization carries information about the magnetic fields in interstellar
clouds. The observations of polarized dust emission are used to study the role
of magnetic fields in the evolution of molecular clouds and the initial phases
of star-formation. We study the grain alignment with realistic simulations,
assuming the radiative torques to be the main mechanism that spins the grains
up. The aim is to study the efficiency of the grain alignment as a function of
cloud position and to study the observable consequences of these spatial
variations. Our results are based on the analysis of model clouds derived from
MHD simulations. The continuum radiative transfer problem is solved with Monte
Carlo methods to estimate the 3D distribution of dust emission and the
radiation field strength affecting the grain alignment. We also examine the
effect of grain growth in cores. We are able to reproduce the results of Cho &
Lazarian using their assumptions. However, the anisotropy factor even in the 1D
case is lower than their assumption of , and thus we get less
efficient radiative torques. Compared with our previous paper, the polarization
degree vs. intensity relation is steeper because of less efficient grain
alignment within dense cores. Without grain growth, the magnetic field of the
cores is poorly recovered above a few . If grain size is doubled in
the cores, the polarization of dust emission can trace the magnetic field lines
possibly up to magnitudes. However, many of the prestellar
cores may be too young for grain coagulation to play a major role. The
inclusion of direction dependent radiative torque efficiency weakens the
alignment. Even with doubled grain size, we would not expect to probe the
magnetic field past a few magnitudes in .Comment: 12 pages, 15 figures, submitted to A&A 19.12.2008; 09.01.2009:
Corrected the name of Juvela; 24.04.2009: revised, added content, 13 pages,
16 figures; 18.06.2009: Language edited, print versio
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
We consider a class of singular Liouville equations on compact surfaces
motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the
Gaussian curvature prescription with conical singularities and Onsager's
description of turbulence. We analyse the problem of existence variationally,
and show how the angular distribution of the conformal volume near the
singularities may lead to improvements in the Moser-Trudinger inequality, and
in turn to lower bounds on the Euler-Lagrange functional. We then discuss
existence and non-existence results.Comment: some references adde
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