168 research outputs found
Self-intersecting marginally outer trapped surfaces
We have shown previously that a merger of marginally outer trapped surfaces (MOTSs) occurs in a binary black hole merger and that there is a continuous sequence of MOTSs which connects the initial two black holes to the final one. In this paper, we confirm this scenario numerically and we detail further improvements in the numerical methods for locating MOTSs. With these improvements, we confirm the merger scenario and demonstrate the existence of self-intersecting MOTSs formed in the immediate aftermath of the merger. These results will allow us to track physical quantities across the non-linear merger process and to potentially infer properties of the merger from gravitational wave observations
The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes
It is well known that quasi-local black hole horizons depend on the choice of
a time coordinate in a spacetime. This has implications for notions such as the
surface of the black hole and also on quasi-local physical quantities such as
horizon measures of mass and angular momentum. In this paper, we compare
different horizons on non-spherically symmetric slicings of Vaidya spacetimes.
The spacetimes we investigate include both accreting and evaporating black
holes. For some simple choices of the Vaidya mass function function
corresponding to collapse of a hollow shell, we compare the area for the
numerically found axisymmetric trapping horizons with the area of the
spherically symmetric trapping horizon and event horizon. We find that as
expected, both the location and area are dependent on the choice of foliation.
However, the area variation is not large, of order for a slowly
evolving horizon with . We also calculate analytically the
difference in area between the spherically symmetric quasi-local horizon and
event horizon for a slowly accreting black hole. We find that the difference
can be many orders of magnitude larger than the Planck area for sufficiently
large black holes.Comment: 10 pages, 5 figures, corrected minor typo
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
The runaway instability in general relativistic accretion disks
When an accretion disk falls prey to the runaway instability, a large portion
of its mass is devoured by the black hole within a few dynamical times. Despite
decades of effort, it is still unclear under what conditions such an
instability can occur. The technically most advanced relativistic simulations
to date were unable to find a clear sign for the onset of the instability. In
this work, we present three-dimensional relativistic hydrodynamics simulations
of accretion disks around black holes in dynamical space-time. We focus on the
configurations that are expected to be particularly prone to the development of
this instability. We demonstrate, for the first time, that the fully
self-consistent general relativistic evolution does indeed produce a runaway
instability.Comment: 5 pages, 3 figures, minor corrections to match published version in
MNRAS, +link to animatio
Computational Relativistic Astrophysics With Adaptive Mesh Refinement: Testbeds
We have carried out numerical simulations of strongly gravitating systems
based on the Einstein equations coupled to the relativistic hydrodynamic
equations using adaptive mesh refinement (AMR) techniques. We show AMR
simulations of NS binary inspiral and coalescence carried out on a workstation
having an accuracy equivalent to that of a regular unigrid simulation,
which is, to the best of our knowledge, larger than all previous simulations of
similar NS systems on supercomputers. We believe the capability opens new
possibilities in general relativistic simulations.Comment: 7 pages, 16 figure
Two physical characteristics of numerical apparent horizons
This article translates some recent results on quasilocal horizons into the
language of general relativity so as to make them more useful to
numerical relativists. In particular quantities are described which
characterize how quickly an apparent horizon is evolving and how close it is to
either equilibrium or extremality.Comment: 6 pages, 2 figures, conference proceedings loosely based on talk
given at Theory Canada III (Edmonton, Alberta, 2007). V2: Minor changes in
response to referees comments to improve clarity and fix typos. One reference
adde
The spatial relation between the event horizon and trapping horizon
The relation between event horizons and trapping horizons is investigated in
a number of different situations with emphasis on their role in thermodynamics.
A notion of constant change is introduced that in certain situations allows the
location of the event horizon to be found locally. When the black hole is
accreting matter the difference in area between the two different horizons can
be many orders of magnitude larger than the Planck area. When the black hole is
evaporating the difference is small on the Planck scale. A model is introduced
that shows how trapping horizons can be expected to appear outside the event
horizon before the black hole starts to evaporate. Finally a modified
definition is introduced to invariantly define the location of the trapping
horizon under a conformal transformation. In this case the trapping horizon is
not always a marginally outer trapped surface.Comment: 16 pages, 1 figur
High accuracy binary black hole simulations with an extended wave zone
We present results from a new code for binary black hole evolutions using the
moving-puncture approach, implementing finite differences in generalised
coordinates, and allowing the spacetime to be covered with multiple
communicating non-singular coordinate patches. Here we consider a regular
Cartesian near zone, with adapted spherical grids covering the wave zone. The
efficiencies resulting from the use of adapted coordinates allow us to maintain
sufficient grid resolution to an artificial outer boundary location which is
causally disconnected from the measurement. For the well-studied test-case of
the inspiral of an equal-mass non-spinning binary (evolved for more than 8
orbits before merger), we determine the phase and amplitude to numerical
accuracies better than 0.010% and 0.090% during inspiral, respectively, and
0.003% and 0.153% during merger. The waveforms, including the resolved higher
harmonics, are convergent and can be consistently extrapolated to
throughout the simulation, including the merger and ringdown. Ringdown
frequencies for these modes (to ) match perturbative
calculations to within 0.01%, providing a strong confirmation that the remnant
settles to a Kerr black hole with irreducible mass and spin $S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}
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
- …