491 research outputs found
Schwarzschild-de Sitter Spacetimes, McVittie Coordinates, and Trumpet Geometries
Trumpet geometries play an important role in numerical simulations of black
hole spacetimes, which are usually performed under the assumption of asymptotic
flatness. Our Universe is not asymptotically flat, however, which has motivated
numerical studies of black holes in asymptotically de Sitter spacetimes. We
derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter
spacetimes by first generalizing the static maximal trumpet slicing of the
Schwarzschild spacetime to static constant mean curvature trumpet slicings of
Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic
radial coordinate which results in a coordinate system analogous to McVittie
coordinates. At large distances from the black hole the resulting metric
asymptotes to a Friedmann-Lemaitre-Robertson-Walker metric with an
exponentially-expanding scale factor. While McVittie coordinates have another
asymptotically de Sitter end as the radial coordinate goes to zero, so that
they generalize the notion of a "wormhole" geometry, our new coordinates
approach a horizon-penetrating trumpet geometry in the same limit. Our
analytical expressions clarify the role of time-dependence, boundary conditions
and coordinate conditions for trumpet slices in a cosmological context, and
provide a useful test for black hole simulations in asymptotically de Sitter
spacetimes.Comment: 7 pages, 3 figures, added referenc
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
Trumpet Slices in Kerr Spacetimes
We introduce a new time-independent family of analytical coordinate systems
for the Kerr spacetime representing rotating black holes. We also propose a
(2+1)+1 formalism for the characterization of trumpet geometries. Applying this
formalism to our new family of coordinate systems we identify, for the first
time, analytical and stationary trumpet slices for general rotating black
holes, even for charged black holes in the presence of a cosmological constant.
We present results for metric functions in this slicing and analyze the
geometry of the rotating trumpet surface.Comment: 5 pages, 2 figures; version published in PR
Approximate initial data for binary black holes
We construct approximate analytical solutions to the constraint equations of
general relativity for binary black holes of arbitrary mass ratio in
quasicircular orbit. We adopt the puncture method to solve the constraint
equations in the transverse-traceless decomposition and consider perturbations
of Schwarzschild black holes caused by boosts and the presence of a binary
companion. A superposition of these two perturbations then yields approximate,
but fully analytic binary black hole initial data that are accurate to first
order in the inverse of the binary separation and the square of the black
holes' momenta.Comment: 13 pages, 4 figures, added comparison to numerical calculations,
accepted to PR
Gravitational Wavetrains in the Quasi-Equilibrium Approximation: A Model Problem in Scalar Gravitation
A quasi-equilibrium (QE) computational scheme was recently developed in
general relativity to calculate the complete gravitational wavetrain emitted
during the inspiral phase of compact binaries. The QE method exploits the fact
that the the gravitational radiation inspiral timescale is much longer than the
orbital period everywhere outside the ISCO. Here we demonstrate the validity
and advantages of the QE scheme by solving a model problem in relativistic
scalar gravitation theory. By adopting scalar gravitation, we are able to
numerically track without approximation the damping of a simple, quasi-periodic
radiating system (an oscillating spherical matter shell) to final equilibrium,
and then use the exact numerical results to calibrate the QE approximation
method. In particular, we calculate the emitted gravitational wavetrain three
different ways: by integrating the exact coupled dynamical field and matter
equations, by using the scalar-wave monopole approximation formula
(corresponding to the quadrupole formula in general relativity), and by
adopting the QE scheme. We find that the monopole formula works well for weak
field cases, but fails when the fields become even moderately strong. By
contrast, the QE scheme remains quite reliable for moderately strong fields,
and begins to breakdown only for ultra-strong fields. The QE scheme thus
provides a promising technique to construct the complete wavetrain from binary
inspiral outside the ISCO, where the gravitational fields are strong, but where
the computational resources required to follow the system for more than a few
orbits by direct numerical integration of the exact equations are prohibitive.Comment: 15 pages, 14 figure
Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test
We include matter sources in Einstein's field equations and show that our
recently proposed 3+1 evolution scheme can stably evolve strong-field
solutions. We insert in our code known matter solutions, namely the
Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder
solution for homogeneous dust sphere collapse to a black hole, and evolve the
gravitational field equations. We find that we can evolve stably static,
strong-field stars for arbitrarily long times and can follow dust sphere
collapse accurately well past black hole formation. These tests are useful
diagnostics for fully self-consistent, stable hydrodynamical simulations in 3+1
general relativity. Moreover, they suggest a successive approximation scheme
for determining gravitational waveforms from strong-field sources dominated by
longitudinal fields, like binary neutron stars: approximate quasi-equilibrium
models can serve as sources for the transverse field equations, which can be
evolved without having to re-solve the hydrodynamical equations (``hydro
without hydro'').Comment: 4 postscript figures. Submitted to Phys. Rev. D15 as a Brief Repor
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
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
Trumpet slices of the Schwarzschild-Tangherlini spacetime
We study families of time-independent maximal and 1+log foliations of the
Schwarzschild-Tangherlini spacetime, the spherically-symmetric vacuum black
hole solution in D spacetime dimensions, for D >= 4. We identify special
members of these families for which the spatial slices display a trumpet
geometry. Using a generalization of the 1+log slicing condition that is
parametrized by a constant n we recover the results of Nakao, Abe, Yoshino and
Shibata in the limit of maximal slicing. We also construct a numerical code
that evolves the BSSN equations for D=5 in spherical symmetry using
moving-puncture coordinates, and demonstrate that these simulations settle down
to the trumpet solutions.Comment: 11 pages, 6 figures, submitted to PR
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