20 research outputs found
Binary Black Hole Encounters, Gravitational Bursts and Maximum Final Spin
The spin of the final black hole in the coalescence of nonspinning black
holes is determined by the ``residual'' orbital angular momentum of the binary.
This residual momentum consists of the orbital angular momentum that the binary
is not able to shed in the process of merging. We study the angular momentum
radiated, the spin of the final black hole and the gravitational bursts in a
series of orbits ranging from almost direct infall to numerous orbits before
infall that exhibit multiple bursts of radiation in the merger process. We show
that the final black hole gets a maximum spin parameter , and
this maximum occurs for initial orbital angular momentum .Comment: Replaced with version to appear in PR
Toward a dynamical shift condition for unequal mass black hole binary simulations
Moving puncture simulations of black hole binaries rely on a specific gauge
choice that leads to approximately stationary coordinates near each black hole.
Part of the shift condition is a damping parameter, which has to be properly
chosen for stable evolutions. However, a constant damping parameter does not
account for the difference in mass in unequal mass binaries. We introduce a
position dependent shift damping that addresses this problem. Although the
coordinates change, the changes in the extracted gravitational waves are small.Comment: 15 pages, submitted to CQG for NRDA 2009 conference proceeding
Unequal Mass Binary Black Hole Plunges and Gravitational Recoil
We present results from fully nonlinear simulations of unequal mass binary
black holes plunging from close separations well inside the innermost stable
circular orbit with mass ratios q = M_1/M_2 = {1,0.85,0.78,0.55,0.32}, or
equivalently, with reduced mass parameters . For each case, the initial binary orbital
parameters are chosen from the Cook-Baumgarte equal-mass ISCO configuration. We
show waveforms of the dominant l=2,3 modes and compute estimates of energy and
angular momentum radiated. For the plunges from the close separations
considered, we measure kick velocities from gravitational radiation recoil in
the range 25-82 km/s. Due to the initial close separations our kick velocity
estimates should be understood as a lower bound. The close configurations
considered are also likely to contain significant eccentricities influencing
the recoil velocity.Comment: 12 pages, 5 figures, to appear in "New Frontiers" special issue of
CQ
Momentum constraint relaxation
Full relativistic simulations in three dimensions invariably develop runaway
modes that grow exponentially and are accompanied by violations of the
Hamiltonian and momentum constraints. Recently, we introduced a numerical
method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint
violation and helps improve the quality of the numerical model. We present here
a method that controls the violation of the momentum constraint. The method is
based on the addition of a longitudinal component to the traceless extrinsic
curvature generated by a vector potential w_i, as outlined by York. The
components of w_i are relaxed to solve approximately the momentum constraint
equations, pushing slowly the evolution toward the space of solutions of the
constraint equations. We test this method with simulations of binary neutron
stars in circular orbits and show that effectively controls the growth of the
aforementioned violations. We also show that a full numerical enforcement of
the constraints, as opposed to the gentle correction of the momentum relaxation
scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More
detailed description of the algorithms are provided. Final published versio
Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
We study gravitational perturbations of Schwarzschild spacetime by solving a
hyperboloidal initial value problem for the Bardeen-Press equation.
Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us
to have access to the gravitational waveform at null infinity in a general
setup. We argue that this hyperboloidal approach leads to a more accurate and
efficient calculation of the radiation signal than the common approach where a
timelike outer boundary is introduced. The method can be generalized to study
perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure
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
Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
A numerical solution scheme for the Einstein field equations based on
generalized harmonic coordinates is described, focusing on details not provided
before in the literature and that are of particular relevance to the binary
black hole problem. This includes demonstrations of the effectiveness of
constraint damping, and how the time slicing can be controlled through the use
of a source function evolution equation. In addition, some results from an
ongoing study of binary black hole coalescence, where the black holes are
formed via scalar field collapse, are shown. Scalar fields offer a convenient
route to exploring certain aspects of black hole interactions, and one
interesting, though tentative suggestion from this early study is that behavior
reminiscent of "zoom-whirl" orbits in particle trajectories is also present in
the merger of equal mass, non-spinning binaries, with appropriately fine-tuned
initial conditions.Comment: 16 pages, 14 figures; replaced with published versio
Phenomenological template family for black-hole coalescence waveforms
Recent progress in numerical relativity has enabled us to model the
non-perturbative merger phase of the binary black-hole coalescence problem.
Based on these results, we propose a phenomenological family of waveforms which
can model the inspiral, merger, and ring-down stages of black hole coalescence.
We also construct a template bank using this family of waveforms and discuss
its implementation in the search for signatures of gravitational waves produced
by black-hole coalescences in the data of ground-based interferometers. This
template bank might enable us to extend the present inspiral searches to
higher-mass binary black-hole systems, i.e., systems with total mass greater
than about 80 solar masses, thereby increasing the reach of the current
generation of ground-based detectors.Comment: Minor changes, Submitted to Class. Quantum Grav. (Proc. GWDAW11
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
Towards absorbing outer boundaries in General Relativity
We construct exact solutions to the Bianchi equations on a flat spacetime
background. When the constraints are satisfied, these solutions represent in-
and outgoing linearized gravitational radiation. We then consider the Bianchi
equations on a subset of flat spacetime of the form [0,T] x B_R, where B_R is a
ball of radius R, and analyze different kinds of boundary conditions on
\partial B_R. Our main results are: i) We give an explicit analytic example
showing that boundary conditions obtained from freezing the incoming
characteristic fields to their initial values are not compatible with the
constraints. ii) With the help of the exact solutions constructed, we determine
the amount of artificial reflection of gravitational radiation from
constraint-preserving boundary conditions which freeze the Weyl scalar Psi_0 to
its initial value. For monochromatic radiation with wave number k and arbitrary
angular momentum number l >= 2, the amount of reflection decays as 1/(kR)^4 for
large kR. iii) For each L >= 2, we construct new local constraint-preserving
boundary conditions which perfectly absorb linearized radiation with l <= L.
(iv) We generalize our analysis to a weakly curved background of mass M, and
compute first order corrections in M/R to the reflection coefficients for
quadrupolar odd-parity radiation. For our new boundary condition with L=2, the
reflection coefficient is smaller than the one for the freezing Psi_0 boundary
condition by a factor of M/R for kR > 1.04. Implications of these results for
numerical simulations of binary black holes on finite domains are discussed.Comment: minor revisions, 30 pages, 6 figure