144 research outputs found
A trapped surface in the higher-dimensional self-similar Vaidya spacetime
We investigate a trapped surface and naked singularity in a -dimensional
Vaidya spacetime with a self-similar mass function. A trapped surface is
defined as a closed spacelike -surface which has negative both null
expansions. There is no trapped surface in the Minkowski spacetime. However, in
a four-dimensional self-similar Vaidya spacetime, Bengtsson and Senovilla
considered non-spherical trapped surfaces and showed that a trapped surface can
penetrate into a flat region, if and only if the mass function rises fast
enough [I. Bengtsson and J. M. M. Senovilla, Phys. Rev. D \textbf{79}, 024027
(2009).]. We apply this result to a -dimensional spacetime motivated by the
context of large extra dimensions or TeV-scale gravity. In this paper,
similarly to Bengtsson and Senovilla's study, we match four types of
-surfaces and show that a trapped surface extended into the flat region
can be constructed in the -dimensional Vaidya spacetime, if the increasing
rate of the mass function is greater than 0.4628. Moreover, we show that the
maximum radius of the trapped surface constructed here approaches the
Schwarzschild-Tangherlini radius in the large limit. Also, we show that
there is no naked singularity, if the spacetime has the trapped surface
constructed here.Comment: 13 pages, 5 figure
New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
We construct new, efficient, and accurate high-order finite differencing
operators which satisfy summation by parts. Since these operators are not
uniquely defined, we consider several optimization criteria: minimizing the
bandwidth, the truncation error on the boundary points, the spectral radius, or
a combination of these. We examine in detail a set of operators that are up to
tenth order accurate in the interior, and we surprisingly find that a
combination of these optimizations can improve the operators' spectral radius
and accuracy by orders of magnitude in certain cases. We also construct
high-order dissipation operators that are compatible with these new finite
difference operators and which are semi-definite with respect to the
appropriate summation by parts scalar product. We test the stability and
accuracy of these new difference and dissipation operators by evolving a
three-dimensional scalar wave equation on a spherical domain consisting of
seven blocks, each discretized with a structured grid, and connected through
penalty boundary conditions.Comment: 16 pages, 9 figures. The files with the coefficients for the
derivative and dissipation operators can be accessed by downloading the
source code for the document. The files are located in the "coeffs"
subdirector
Horizon Pretracking
We introduce horizon pretracking as a method for analysing numerically
generated spacetimes of merging black holes. Pretracking consists of following
certain modified constant expansion surfaces during a simulation before a
common apparent horizon has formed. The tracked surfaces exist at all times,
and are defined so as to include the common apparent horizon if it exists. The
method provides a way for finding this common apparent horizon in an efficient
and reliable manner at the earliest possible time. We can distinguish inner and
outer horizons by examining the distortion of the surface. Properties of the
pretracking surface such as its expansion, location, shape, area, and angular
momentum can also be used to predict when a common apparent horizon will
appear, and its characteristics. The latter could also be used to feed back
into the simulation by adapting e.g. boundary or gauge conditions even before
the common apparent horizon has formed.Comment: 14 pages, 8 figures, minor change
Numerical relativity with characteristic evolution, using six angular patches
The characteristic approach to numerical relativity is a useful tool in
evolving gravitational systems. In the past this has been implemented using two
patches of stereographic angular coordinates. In other applications, a
six-patch angular coordinate system has proved effective. Here we investigate
the use of a six-patch system in characteristic numerical relativity, by
comparing an existing two-patch implementation (using second-order finite
differencing throughout) with a new six-patch implementation (using either
second- or fourth-order finite differencing for the angular derivatives). We
compare these different codes by monitoring the Einstein constraint equations,
numerically evaluated independently from the evolution. We find that, compared
to the (second-order) two-patch code at equivalent resolutions, the errors of
the second-order six-patch code are smaller by a factor of about 2, and the
errors of the fourth-order six-patch code are smaller by a factor of nearly 50.Comment: 12 pages, 5 figures, submitted to CQG (special NFNR issue
Binary neutron-star mergers with Whisky and SACRA: First quantitative comparison of results from independent general-relativistic hydrodynamics codes
We present the first quantitative comparison of two independent
general-relativistic hydrodynamics codes, the Whisky code and the SACRA code.
We compare the output of simulations starting from the same initial data and
carried out with the configuration (numerical methods, grid setup, resolution,
gauges) which for each code has been found to give consistent and sufficiently
accurate results, in particular in terms of cleanness of gravitational
waveforms. We focus on the quantities that should be conserved during the
evolution (rest mass, total mass energy, and total angular momentum) and on the
gravitational-wave amplitude and frequency. We find that the results produced
by the two codes agree at a reasonable level, with variations in the different
quantities but always at better than about 10%.Comment: Published on Phys. Rev.
Black hole head-on collisions and gravitational waves with fixed mesh-refinement and dynamic singularity excision
We present long-term-stable and convergent evolutions of head-on black hole
collisions and extraction of gravitational waves generated during the merger
and subsequent ring-down. The new ingredients in this work are the use of fixed
mesh-refinement and dynamical singularity excision techniques. We are able to
carry out head-on collisions with large initial separations and demonstrate
that our excision infrastructure is capable of accommodating the motion of the
individual black holes across the computational domain as well as their their
merger. We extract gravitational waves from these simulations using the
Zerilli-Moncrief formalism and find the ring-down radiation to be, as expected,
dominated by the l=2, m=0 quasi-normal mode. The total radiated energy is about
0.1 % of the total ADM mass of the system.Comment: Revised version, 1 figure added, accepted for publication in
Phys.Rev.D, 15 pages, 10 figures, revtex 4.
Introduction to dynamical horizons in numerical relativity
This paper presents a quasi-local method of studying the physics of dynamical
black holes in numerical simulations. This is done within the dynamical horizon
framework, which extends the earlier work on isolated horizons to
time-dependent situations. In particular: (i) We locate various kinds of
marginal surfaces and study their time evolution. An important ingredient is
the calculation of the signature of the horizon, which can be either spacelike,
timelike, or null. (ii) We generalize the calculation of the black hole mass
and angular momentum, which were previously defined for axisymmetric isolated
horizons to dynamical situations. (iii) We calculate the source multipole
moments of the black hole which can be used to verify that the black hole
settles down to a Kerr solution. (iv) We also study the fluxes of energy
crossing the horizon, which describes how a black hole grows as it accretes
matter and/or radiation.
We describe our numerical implementation of these concepts and apply them to
three specific test cases, namely, the axisymmetric head-on collision of two
black holes, the axisymmetric collapse of a neutron star, and a
non-axisymmetric black hole collision with non-zero initial orbital angular
momentum.Comment: 20 pages, 16 figures, revtex4. Several smaller changes, some didactic
content shortene
Moving black holes via singularity excision
We present a singularity excision algorithm appropriate for numerical
simulations of black holes moving throughout the computational domain. The
method is an extension of the excision procedure previously used to obtain
stable simulations of single, non-moving black holes. The excision procedure
also shares elements used in recent work to study the dynamics of a scalarfield
in the background of a single, boosted black hole. The robustness of our
excision method is tested with single black-hole evolutions using a coordinate
system in which the coordinate location of the black hole, and thus the
excision boundary, moves throughout the computational domain.Comment: 9 pages and 11 figure
BSSN in Spherical Symmetry
The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein
evolution equations is written in spherical symmetry. These equations can be
used to address a number of technical and conceptual issues in numerical
relativity in the context of a single Schwarzschild black hole. One of the
benefits of spherical symmetry is that the numerical grid points can be tracked
on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture
evolution of a Schwarzschild black hole are presented. Several results are
shown for puncture evolution using a fourth--order finite difference
implementation of the equations.Comment: This is the final version to be published in CQG. It contains much
more information and detail than the original versio
- …