978 research outputs found
Hyperboloidal slices for the wave equation of Kerr-Schild metrics and numerical applications
We present new results from two open source codes, using finite differencing
and pseudo-spectral methods for the wave equations in (3+1) dimensions. We use
a hyperboloidal transformation which allows direct access to null infinity and
simplifies the control over characteristic speeds on Kerr-Schild backgrounds.
We show that this method is ideal for attaching hyperboloidal slices or for
adapting the numerical resolution in certain spacetime regions. As an example
application, we study late-time Kerr tails of sub-dominant modes and obtain new
insight into the splitting of decay rates. The involved conformal wave equation
is freed of formally singular terms whose numerical evaluation might be
problematically close to future null infinity.Comment: 15 pages, 12 figure
The 3D Grazing Collision of Two Black Holes
We present results for two colliding black holes (BHs), with angular
momentum, spin, and unequal mass. For the first time gravitational waveforms
are computed for a grazing collision from a full 3D numerical evolution. The
collision can be followed through the merger to form a single BH, and through
part of the ringdown period of the final BH. The apparent horizon is tracked
and studied, and physical parameters, such as the mass of the final BH, are
computed. The total energy radiated in gravitational waves is shown to be
consistent with the total mass of the spacetime and the final BH mass. The
implication of these simulations for gravitational wave astronomy is discussed.Comment: 4 pages, 7 figures, revte
An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates
A number of astrophysical scenarios possess and preserve an overall
cylindrical symmetry also when undergoing a catastrophic and nonlinear
evolution. Exploiting such a symmetry, these processes can be studied through
numerical-relativity simulations at smaller computational costs and at
considerably larger spatial resolutions. We here present a new
flux-conservative formulation of the relativistic hydrodynamics equations in
cylindrical coordinates. By rearranging those terms in the equations which are
the sources of the largest numerical errors, the new formulation yields a
global truncation error which is one or more orders of magnitude smaller than
those of alternative and commonly used formulations. We illustrate this through
a series of numerical tests involving the evolution of oscillating spherical
and rotating stars, as well as shock-tube tests.Comment: 19 pages, 9 figure
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio
Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation
The properties of the Volume operator in Loop Quantum Gravity, as constructed
by Ashtekar and Lewandowski, are analyzed for the first time at generic
vertices of valence greater than four. The present analysis benefits from the
general simplified formula for matrix elements of the Volume operator derived
in gr-qc/0405060, making it feasible to implement it on a computer as a matrix
which is then diagonalized numerically. The resulting eigenvalues serve as a
database to investigate the spectral properties of the volume operator.
Analytical results on the spectrum at 4-valent vertices are included. This is a
companion paper to arXiv:0706.0469, providing details of the analysis presented
there.Comment: Companion to arXiv:0706.0469. Version as published in CQG in 2008.
More compact presentation. Sign factor combinatorics now much better
understood in context of oriented matroids, see arXiv:1003.2348, where also
important remarks given regarding sigma configurations. Subsequent
computations revealed some minor errors, which do not change qualitative
results but modify some numbers presented her
Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity
The accurate modeling of gravitational radiation is a key issue for
gravitational wave astronomy. As simulation codes reach higher accuracy,
systematic errors inherent in current numerical relativity wave-extraction
methods become evident, and may lead to a wrong astrophysical interpretation of
the data. In this paper, we give a detailed description of the
Cauchy-characteristic extraction technique applied to binary black hole
inspiral and merger evolutions to obtain gravitational waveforms that are
defined unambiguously, that is, at future null infinity. By this method we
remove finite-radius approximations and the need to extrapolate data from the
near zone. Further, we demonstrate that the method is free of gauge effects and
thus is affected only by numerical error. Various consistency checks reveal
that energy and angular momentum are conserved to high precision and agree very
well with extrapolated data. In addition, we revisit the computation of the
gravitational recoil and find that finite radius extrapolation very well
approximates the result at \scri. However, the (non-convergent) systematic
differences to extrapolated data are of the same order of magnitude as the
(convergent) discretisation error of the Cauchy evolution hence highlighting
the need for correct wave-extraction.Comment: 41 pages, 8 figures, 2 tables, added references, fixed typos. Version
matches published version
The Current Status of Binary Black Hole Simulations in Numerical Relativity
Since the breakthroughs in 2005 which have led to long term stable solutions
of the binary black hole problem in numerical relativity, much progress has
been made. I present here a short summary of the state of the field, including
the capabilities of numerical relativity codes, recent physical results
obtained from simulations, and improvements to the methods used to evolve and
analyse binary black hole spacetimes.Comment: 14 pages; minor changes and corrections in response to referee
Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity
We analyze combinatorial structures which play a central role in determining
spectral properties of the volume operator in loop quantum gravity (LQG). These
structures encode geometrical information of the embedding of arbitrary valence
vertices of a graph in 3-dimensional Riemannian space, and can be represented
by sign strings containing relative orientations of embedded edges. We
demonstrate that these signature factors are a special representation of the
general mathematical concept of an oriented matroid. Moreover, we show that
oriented matroids can also be used to describe the topology (connectedness) of
directed graphs. Hence the mathematical methods developed for oriented matroids
can be applied to the difficult combinatorics of embedded graphs underlying the
construction of LQG. As a first application we revisit the analysis of [4-5],
and find that enumeration of all possible sign configurations used there is
equivalent to enumerating all realizable oriented matroids of rank 3, and thus
can be greatly simplified. We find that for 7-valent vertices having no
coplanar triples of edge tangents, the smallest non-zero eigenvalue of the
volume spectrum does not grow as one increases the maximum spin \jmax at the
vertex, for any orientation of the edge tangents. This indicates that, in
contrast to the area operator, considering large \jmax does not necessarily
imply large volume eigenvalues. In addition we give an outlook to possible
starting points for rewriting the combinatorics of LQG in terms of oriented
matroids.Comment: 43 pages, 26 figures, LaTeX. Version published in CQG. Typos
corrected, presentation slightly extende
Measurement of the cross-section and charge asymmetry of bosons produced in proton-proton collisions at TeV with the ATLAS detector
This paper presents measurements of the and cross-sections and the associated charge asymmetry as a
function of the absolute pseudorapidity of the decay muon. The data were
collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with
the ATLAS experiment at the LHC and correspond to a total integrated luminosity
of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements
varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the
1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured
with an uncertainty between 0.002 and 0.003. The results are compared with
predictions based on next-to-next-to-leading-order calculations with various
parton distribution functions and have the sensitivity to discriminate between
them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables,
submitted to EPJC. All figures including auxiliary figures are available at
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13
Search for chargino-neutralino production with mass splittings near the electroweak scale in three-lepton final states in √s=13 TeV pp collisions with the ATLAS detector
A search for supersymmetry through the pair production of electroweakinos with mass splittings near the electroweak scale and decaying via on-shell W and Z bosons is presented for a three-lepton final state. The analyzed proton-proton collision data taken at a center-of-mass energy of √s=13 TeV were collected between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. A search, emulating the recursive jigsaw reconstruction technique with easily reproducible laboratory-frame variables, is performed. The two excesses observed in the 2015–2016 data recursive jigsaw analysis in the low-mass three-lepton phase space are reproduced. Results with the full data set are in agreement with the Standard Model expectations. They are interpreted to set exclusion limits at the 95% confidence level on simplified models of chargino-neutralino pair production for masses up to 345 GeV
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