1,646 research outputs found
Explicit solution of the linearized Einstein equations in TT gauge for all multipoles
We write out the explicit form of the metric for a linearized gravitational
wave in the transverse-traceless gauge for any multipole, thus generalizing the
well-known quadrupole solution of Teukolsky. The solution is derived using the
generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.Comment: 9 pages. Minor corrections, updated references. Final version to
appear in Class. Quantum Gra
Regularity of the Einstein Equations at Future Null Infinity
When Einstein's equations for an asymptotically flat, vacuum spacetime are
reexpressed in terms of an appropriate conformal metric that is regular at
(future) null infinity, they develop apparently singular terms in the
associated conformal factor and thus appear to be ill-behaved at this
(exterior) boundary. In this article however we show, through an enforcement of
the Hamiltonian and momentum constraints to the needed order in a Taylor
expansion, that these apparently singular terms are not only regular at the
boundary but can in fact be explicitly evaluated there in terms of conformally
regular geometric data. Though we employ a rather rigidly constrained and gauge
fixed formulation of the field equations, we discuss the extent to which we
expect our results to have a more 'universal' significance and, in particular,
to be applicable, after minor modifications, to alternative formulations.Comment: 43 pages, no figures, AMS-TeX. Minor revisions, updated to agree with
published versio
Implementation of higher-order absorbing boundary conditions for the Einstein equations
We present an implementation of absorbing boundary conditions for the
Einstein equations based on the recent work of Buchman and Sarbach. In this
paper, we assume that spacetime may be linearized about Minkowski space close
to the outer boundary, which is taken to be a coordinate sphere. We reformulate
the boundary conditions as conditions on the gauge-invariant
Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated
by rewriting the boundary conditions as a system of ODEs for a set of auxiliary
variables intrinsic to the boundary. From these we construct boundary data for
a set of well-posed constraint-preserving boundary conditions for the Einstein
equations in a first-order generalized harmonic formulation. This construction
has direct applications to outer boundary conditions in simulations of isolated
systems (e.g., binary black holes) as well as to the problem of
Cauchy-perturbative matching. As a test problem for our numerical
implementation, we consider linearized multipolar gravitational waves in TT
gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We
demonstrate that the perfectly absorbing boundary condition B_L of order L=l
yields no spurious reflections to linear order in perturbation theory. This is
in contrast to the lower-order absorbing boundary conditions B_L with L<l,
which include the widely used freezing-Psi_0 boundary condition that imposes
the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in
Class. Quantum Grav
On the Hoop conjecture and the weak cosmic censorship conjecture for the axisymmetric Einstein-Vlasov system
We consider gravitational collapse for the axially symmetric Einstein-Vlasov
system. We investigate the weak cosmic censorship conjecture in the case of
highly prolate initial data and we investigate the ``only if" part of the Hoop
conjecture. Shapiro and Teukolsky initiated a similar study in 1991
\cite{Shapiro1991} where they found support that the weak cosmic censorship
conjecture was violated for sufficiently prolate spheroidal initial data. More
recently, independent studies of this problem have been carried out by Yoo,
Harada and Okawa \cite{Yoo2017} and by East \cite{East2019}. A common feature
in these works is that the initial data are dust-like. Dust can be considered
as a \textit{singular} case of matter described by the Einstein-Vlasov system.
The original motivation by Shapiro and Teukolsky to study this problem is based
on the Lin-Mestel-Shu instability for gravitational collapse of uniform
spheroids in the case of dust in Newtonian gravity. We argue that the
Lin-Mestel-Shu solution is not relevant for studying the weak cosmic censorship
of the Einstein-Vlasov system and we argue that dust-like initial data is also
not relevant. To investigate collapse of highly prolate spheroidal
configurations for the Einstein-Vlasov system is nevertheless interesting in
view of the Hoop conjecture. By choosing highly prolate initial data the weak
cosmic censorship conjecture is seriously tested. We carry out such a study for
initial data which are not dust-like. We find formation of an apparent horizon
in all cases we consider, which provides support for the weak cosmic censorship
conjecture. In our tests of the Hoop conjecture we compute the polar
circumference at the time when the apparent horizon forms
and find that it is less than 12% above , where is the irreducible
mass of the apparent horizon, which agrees with the spirit of the Hoop
conjecture.Comment: 18 pages, 7 figure
Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
This paper is concerned with the initial-boundary value problem for the
Einstein equations in a first-order generalized harmonic formulation. We impose
boundary conditions that preserve the constraints and control the incoming
gravitational radiation by prescribing data for the incoming fields of the Weyl
tensor. High-frequency perturbations about any given spacetime (including a
shift vector with subluminal normal component) are analyzed using the
Fourier-Laplace technique. We show that the system is boundary-stable. In
addition, we develop a criterion that can be used to detect weak instabilities
with polynomial time dependence, and we show that our system does not suffer
from such instabilities. A numerical robust stability test supports our claim
that the initial-boundary value problem is most likely to be well-posed even if
nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added,
several minor amendments; version accepted for publication in Class. Quantum
Gra
Measurements of hydrocarbon emissions from a boreal fen using the REA technique
International audienceFluxes of biogenic volatile organic compounds (VOC) and methane were measured above a boreal fen. Vegetation on the fen is dominated by Sphagnum mosses and sedges. A relaxed eddy accumulation (REA) system with dynamic deadband was designed and constructed for the measurements. Methane, C2-C6 hydrocarbons and some halogenated hydrocarbons were analysed from the samples by gas chromatographs equipped with FID and ECD. A significant flux of isoprene and methane was detected during the growing seasons. Isoprene emission was found to follow the common isoprene emission algorithm. Average standard emission potential of isoprene was 680 ? g m-2h-1. Fluxes of other non-methane hydrocarbons were below detection limit
Testing outer boundary treatments for the Einstein equations
Various methods of treating outer boundaries in numerical relativity are
compared using a simple test problem: a Schwarzschild black hole with an
outgoing gravitational wave perturbation. Numerical solutions computed using
different boundary treatments are compared to a `reference' numerical solution
obtained by placing the outer boundary at a very large radius. For each
boundary treatment, the full solutions including constraint violations and
extracted gravitational waves are compared to those of the reference solution,
thereby assessing the reflections caused by the artificial boundary. These
tests use a first-order generalized harmonic formulation of the Einstein
equations. Constraint-preserving boundary conditions for this system are
reviewed, and an improved boundary condition on the gauge degrees of freedom is
presented. Alternate boundary conditions evaluated here include freezing the
incoming characteristic fields, Sommerfeld boundary conditions, and the
constraint-preserving boundary conditions of Kreiss and Winicour. Rather
different approaches to boundary treatments, such as sponge layers and spatial
compactification, are also tested. Overall the best treatment found here
combines boundary conditions that preserve the constraints, freeze the
Newman-Penrose scalar Psi_0, and control gauge reflections.Comment: Modified to agree with version accepted for publication in Class.
Quantum Gra
An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
We present the first stable dynamical numerical evolutions of the Einstein
equations in terms of a conformally rescaled metric on hyperboloidal
hypersurfaces extending to future null infinity. Axisymmetry is imposed in
order to reduce the computational cost. The formulation is based on an earlier
axisymmetric evolution scheme, adapted to time slices of constant mean
curvature. Ideas from a previous study by Moncrief and the author are applied
in order to regularize the formally singular evolution equations at future null
infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime
are obtained, including a gravitational perturbation. The Bondi news function
is evaluated at future null infinity.Comment: 21 pages, 4 figures. Minor additions, updated to agree with journal
versio
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a
test-bed for constraint-preserving boundary conditions in the non-linear
regime. As an illustration, energy-constraint preservation is separately tested
in the Z4 framework. Both algebraic conditions, derived from energy estimates,
and derivative conditions, deduced from the constraint-propagation system, are
considered. The numerical errors at the boundary are of the same order than
those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting
200
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