519 research outputs found
Spectral Characteristic Evolution: A New Algorithm for Gravitational Wave Propagation
We present a spectral algorithm for solving the full nonlinear vacuum
Einstein field equations in the Bondi framework. Developed within the Spectral
Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a
technical precursor to Cauchy Characteristic Extraction (CCE), a rigorous
method for obtaining gauge-invariant gravitational waveforms from existing and
future astrophysical simulations. We demonstrate the new algorithm's stability,
convergence, and agreement with existing evolution methods. We explain how an
innovative spectral approach enables a two orders of magnitude improvement in
computational efficiency.Comment: 28 pages, 9 figure
Spectral Cauchy Characteristic Extraction of strain, news and gravitational radiation flux
We present a new approach for the Cauchy-characteristic extraction of
gravitational radiation strain, news function, and the flux of the
energy-momentum, supermomentum and angular momentum associated with the
Bondi-Metzner-Sachs asymptotic symmetries. In Cauchy-characteristic extraction,
a characteristic evolution code takes numerical data on an inner worldtube
supplied by a Cauchy evolution code, and propagates it outwards to obtain the
space-time metric in a neighborhood of null infinity. The metric is first
determined in a scrambled form in terms of coordinates determined by the Cauchy
formalism. In prior treatments, the waveform is first extracted from this
metric and then transformed into an asymptotic inertial coordinate system. This
procedure provides the physically proper description of the waveform and the
radiated energy but it does not generalize to determine the flux of angular
momentum or supermomentum. Here we formulate and implement a new approach which
transforms the full metric into an asymptotic inertial frame and provides a
uniform treatment of all the radiation fluxes associated with the asymptotic
symmetries. Computations are performed and calibrated using the Spectral
Einstein Code (SpEC).Comment: 30 pages, 17 figure
The Merger of Small and Large Black Holes
We present simulations of binary black holes mergers in which, after the
common outer horizon has formed, the marginally outer trapped surfaces (MOTSs)
corresponding to the individual black holes continue to approach and eventually
penetrate each other. This has very interesting consequences according to
recent results in the theory of MOTSs. Uniqueness and stability theorems imply
that two MOTSs which touch with a common outer normal must be identical. This
suggests a possible dramatic consequence of the collision between a small and
large black hole. If the penetration were to continue to completion then the
two MOTSs would have to coalesce, by some combination of the small one growing
and the big one shrinking. Here we explore the relationship between theory and
numerical simulations, in which a small black hole has halfway penetrated a
large one.Comment: 17 pages, 11 figure
Characteristic extraction tool for gravitational waveforms
We develop and calibrate a characteristic waveform extraction tool whose major improvements and corrections of prior versions allow satisfaction of the accuracy standards required for advanced LIGO data analysis. The extraction tool uses a characteristic evolution code to propagate numerical data on an inner worldtube supplied by a 3+1 Cauchy evolution to obtain the gravitational waveform at null infinity. With the new extraction tool, high accuracy and convergence of the numerical error can be demonstrated for an inspiral and merger of mass M binary black holes even for an extraction worldtube radius as small as R=20M. The tool provides a means for unambiguous comparison between waveforms generated by evolution codes based upon different formulations of the Einstein equations and based upon different numerical approximations
Strategies for the characteristic extraction of gravitational waveforms
We develop, test, and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component Psi4 to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the O(1/r) radiative part of Psi4 in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves
Simulating merging binary black holes with nearly extremal spins
Astrophysically realistic black holes may have spins that are nearly extremal
(i.e., close to 1 in dimensionless units). Numerical simulations of binary
black holes are important tools both for calibrating analytical templates for
gravitational-wave detection and for exploring the nonlinear dynamics of curved
spacetime. However, all previous simulations of binary-black-hole inspiral,
merger, and ringdown have been limited by an apparently insurmountable barrier:
the merging holes' spins could not exceed 0.93, which is still a long way from
the maximum possible value in terms of the physical effects of the spin. In
this paper, we surpass this limit for the first time, opening the way to
explore numerically the behavior of merging, nearly extremal black holes.
Specifically, using an improved initial-data method suitable for binary black
holes with nearly extremal spins, we simulate the inspiral (through 12.5
orbits), merger and ringdown of two equal-mass black holes with equal spins of
magnitude 0.95 antialigned with the orbital angular momentum.Comment: 4 pages, 2 figures, updated with version accepted for publication in
Phys. Rev. D, removed a plot that was incorrectly included at the end of the
article in version v
Well-Posed Initial-Boundary Evolution in General Relativity
Maximally dissipative boundary conditions are applied to the initial-boundary
value problem for Einstein's equations in harmonic coordinates to show that it
is well-posed for homogeneous boundary data and for boundary data that is small
in a linearized sense. The method is implemented as a nonlinear evolution code
which satisfies convergence tests in the nonlinear regime and is robustly
stable in the weak field regime. A linearized version has been stably matched
to a characteristic code to compute the gravitational waveform radiated to
infinity.Comment: 5 pages, 6 figures; added another convergence plot to Fig. 2 + minor
change
Modeling the Black Hole Excision Problem
We analyze the excision strategy for simulating black holes. The problem is
modeled by the propagation of quasi-linear waves in a 1-dimensional spatial
region with timelike outer boundary, spacelike inner boundary and a horizon in
between. Proofs of well-posed evolution and boundary algorithms for a second
differential order treatment of the system are given for the separate pieces
underlying the finite difference problem. These are implemented in a numerical
code which gives accurate long term simulations of the quasi-linear excision
problem. Excitation of long wavelength exponential modes, which are latent in
the problem, are suppressed using conservation laws for the discretized system.
The techniques are designed to apply directly to recent codes for the Einstein
equations based upon the harmonic formulation.Comment: 21 pages, 14 postscript figures, minor contents updat
An Improved Gauge Driver for the Generalized Harmonic Einstein System
A new gauge driver is introduced for the generalized harmonic (GH)
representation of Einstein's equation. This new driver allows a rather general
class of gauge conditions to be implemented in a way that maintains the
hyperbolicity of the combined evolution system. This driver is more stable and
effective, and unlike previous drivers, allows stable evolutions using the
dual-frame evolution technique. Appropriate boundary conditions for this new
gauge driver are constructed, and a new boundary condition for the ``gauge''
components of the spacetime metric in the GH Einstein system is introduced. The
stability and effectiveness of this new gauge driver are demonstrated through
numerical tests, which impose a new damped-wave gauge condition on the
evolutions of single black-hole spacetimes.Comment: v2: final version to be published in PRD; 15 pages, 5 figure
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