300 research outputs found
An alternative approach to solving the Hamiltonian constraint
Solving Einstein's constraint equations for the construction of black hole
initial data requires handling the black hole singularity. Typically, this is
done either with the excision method, in which the black hole interior is
excised from the numerical grid, or with the puncture method, in which the
singular part of the conformal factor is expressed in terms of an analytical
background solution, and the Hamiltonian constraint is then solved for a
correction to the background solution that, usually, is assumed to be regular
everywhere. We discuss an alternative approach in which the Hamiltonian
constraint is solved for an inverse power of the conformal factor. This new
function remains finite everywhere, so that this approach requires neither
excision nor a split into background and correction. In particular, this method
can be used without modification even when the correction to the conformal
factor is singular itself. We demonstrate this feature for rotating black holes
in the trumpet topology.Comment: 5 pages, 4 figures, matches version published in PR
Prompt merger collapse and the maximum mass of neutron stars
We perform hydrodynamical simulations of neutron-star mergers for a large
sample of temperature-dependent, nuclear equations of state, and determine the
threshold mass above which the merger remnant promptly collapses to form a
black hole. We find that, depending on the equation of state, the threshold
mass is larger than the maximum mass of a non-rotating star in isolation by
between 30 and 70 per cent. Our simulations also show that the ratio between
the threshold mass and maximum mass is tightly correlated with the compactness
of the non-rotating maximum-mass configuration. We speculate on how this
relation can be used to derive constraints on neutron-star properties from
future observations.Comment: 6 pages, 3 figures, accepted for publication in Phys. Rev. Let
Radiation of Angular Momentum by Neutrinos from Merged Binary Neutron Stars
We study neutrino emission from the remnant of an inspiraling binary neutron
star following coalescence. The mass of the merged remnant is likely to exceed
the stability limit of a cold, rotating neutron star. However, the angular
momentum of the remnant may also approach or even exceed the Kerr limit, J/M^2
= 1, so that total collapse may not be possible unless some angular momentum is
dissipated. We find that neutrino emission is very inefficient in decreasing
the angular momentum of these merged objects and may even lead to a small
increase in J/M^2. We illustrate these findings with a post-Newtonian,
ellipsoidal model calculation. Simple arguments suggest that the remnant may
form a bar mode instability on a timescale similar to or shorter than the
neutrino emission timescale, in which case the evolution of the remnant will be
dominated by the emission of gravitational waves.Comment: 12 pages AASTeX, 2 figures, to appear in Ap
Computing the Complete Gravitational Wavetrain from Relativistic Binary Inspiral
We present a new method for generating the nonlinear gravitational wavetrain
from the late inspiral (pre-coalescence) phase of a binary neutron star system
by means of a numerical evolution calculation in full general relativity. In a
prototype calculation, we produce 214 wave cycles from corotating polytropes,
representing the final part of the inspiral phase prior to reaching the ISCO.
Our method is based on the inequality that the orbital decay timescale due to
gravitational radiation is much longer than an orbital period and the
approximation that gravitational radiation has little effect on the structure
of the stars. We employ quasi-equilibrium sequences of binaries in circular
orbit for the matter source in our field evolution code. We compute the
gravity-wave energy flux, and, from this, the inspiral rate, at a discrete set
of binary separations. From these data, we construct the gravitational waveform
as a continuous wavetrain. Finally, we discuss the limitations of our current
calculation, planned improvements, and potential applications of our method to
other inspiral scenarios.Comment: 4 pages, 4 figure
Analytical Tendex and Vortex Fields for Perturbative Black Hole Initial Data
Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the
electric and magnetic parts of the Weyl curvature tensor, form the basis of a
recently developed approach to visualizing spacetime curvature. In particular,
this method has been proposed as a tool for interpreting results from numerical
binary black hole simulations, providing a deeper insight into the physical
processes governing the merger of black holes and the emission of gravitational
radiation. Here we apply this approach to approximate but analytical initial
data for both single boosted and binary black holes. These perturbative data
become exact in the limit of small boost or large binary separation. We hope
that these calculations will provide additional insight into the properties of
tendex and vortex fields, and will form a useful test for future numerical
calculations.Comment: 18 pages, 8 figures, submitted to PR
Analytical Representation of a Black Hole Puncture Solution
The ``moving puncture'' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et.al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving puncture simulations, the evolution of a single black hole leads to a well-known time-independent, maximal slicing of Schwarzschild. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example for testing and calibrating numerical codes that employ moving puncture techniques. In this Brief Report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes
The Innermost Stable Circular Orbit of Binary Black Holes
We introduce a new method to construct solutions to the constraint equations
of general relativity describing binary black holes in quasicircular orbit.
Black hole pairs with arbitrary momenta can be constructed with a simple method
recently suggested by Brandt and Bruegmann, and quasicircular orbits can then
be found by locating a minimum in the binding energy along sequences of
constant horizon area. This approach produces binary black holes in a
"three-sheeted" manifold structure, as opposed to the "two-sheeted" structure
in the conformal-imaging approach adopted earlier by Cook. We focus on locating
the innermost stable circular orbit and compare with earlier calculations. Our
results confirm those of Cook and imply that the underlying manifold structure
has a very small effect on the location of the innermost stable circular orbit.Comment: 8 pages, 3 figures, RevTex, submitted to PR
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