558 research outputs found
Generic effective source for scalar self-force calculations
A leading approach to the modelling of extreme mass ratio inspirals involves
the treatment of the smaller mass as a point particle and the computation of a
regularized self-force acting on that particle. In turn, this computation
requires knowledge of the regularized retarded field generated by the particle.
A direct calculation of this regularized field may be achieved by replacing the
point particle with an effective source and solving directly a wave equation
for the regularized field. This has the advantage that all quantities are
finite and require no further regularization. In this work, we present a method
for computing an effective source which is finite and continuous everywhere,
and which is valid for a scalar point particle in arbitrary geodesic motion in
an arbitrary background spacetime. We explain in detail various technical and
practical considerations that underlie its use in several numerical self-force
calculations. We consider as examples the cases of a particle in a circular
orbit about Schwarzschild and Kerr black holes, and also the case of a particle
following a generic time-like geodesic about a highly spinning Kerr black hole.
We provide numerical C code for computing an effective source for various
orbital configurations about Schwarzschild and Kerr black holes.Comment: 24 pages, 7 figures, final published versio
Relativistic MHD and black hole excision: Formulation and initial tests
A new algorithm for solving the general relativistic MHD equations is
described in this paper. We design our scheme to incorporate black hole
excision with smooth boundaries, and to simplify solving the combined Einstein
and MHD equations with AMR. The fluid equations are solved using a finite
difference Convex ENO method. Excision is implemented using overlapping grids.
Elliptic and hyperbolic divergence cleaning techniques allow for maximum
flexibility in choosing coordinate systems, and we compare both methods for a
standard problem. Numerical results of standard test problems are presented in
two-dimensional flat space using excision, overlapping grids, and elliptic and
hyperbolic divergence cleaning.Comment: 22 pages, 8 figure
Evolution of a periodic eight-black-hole lattice in numerical relativity
The idea of black-hole lattices as models for the large-scale structure of
the universe has been under scrutiny for several decades, and some of the
properties of these systems have been elucidated recently in the context of the
problem of cosmological backreaction. The complete, three-dimensional and fully
relativistic evolution of these system has, however, never been tackled. We
explicitly construct the first of these solutions by numerically integrating
Einstein's equation in the case of an eight-black-hole lattice with the
topology of S3.Comment: 21 pages, 13 figures. Corrected and clarified discussio
A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
Gravitational waveforms from the inspiral and ring-down stages of the binary
black hole coalescences can be modelled accurately by
approximation/perturbation techniques in general relativity. Recent progress in
numerical relativity has enabled us to model also the non-perturbative merger
phase of the binary black-hole coalescence problem. This enables us to
\emph{coherently} search for all three stages of the coalescence of
non-spinning binary black holes using a single template bank. Taking our
motivation from these results, we propose a family of template waveforms which
can model the inspiral, merger, and ring-down stages of the coalescence of
non-spinning binary black holes that follow quasi-circular inspiral. This
two-dimensional template family is explicitly parametrized by the physical
parameters of the binary. We show that the template family is not only
\emph{effectual} in detecting the signals from black hole coalescences, but
also \emph{faithful} in estimating the parameters of the binary. We compare the
sensitivity of a search (in the context of different ground-based
interferometers) using all three stages of the black hole coalescence with
other template-based searches which look for individual stages separately. We
find that the proposed search is significantly more sensitive than other
template-based searches for a substantial mass-range, potentially bringing
about remarkable improvement in the event-rate of ground-based interferometers.
As part of this work, we also prescribe a general procedure to construct
interpolated template banks using non-spinning black hole waveforms produced by
numerical relativity.Comment: A typo fixed in Eq.(B11
An Axisymmetric Gravitational Collapse Code
We present a new numerical code designed to solve the Einstein field
equations for axisymmetric spacetimes. The long term goal of this project is to
construct a code that will be capable of studying many problems of interest in
axisymmetry, including gravitational collapse, critical phenomena,
investigations of cosmic censorship, and head-on black hole collisions. Our
objective here is to detail the (2+1)+1 formalism we use to arrive at the
corresponding system of equations and the numerical methods we use to solve
them. We are able to obtain stable evolution, despite the singular nature of
the coordinate system on the axis, by enforcing appropriate regularity
conditions on all variables and by adding numerical dissipation to hyperbolic
equations.Comment: 19 pages, 9 figure
Grazing Collisions of Black Holes via the Excision of Singularities
We present the first simulations of non-headon (grazing) collisions of binary
black holes in which the black hole singularities have been excised from the
computational domain. Initially two equal mass black holes are separated a
distance and with impact parameter . Initial data are
based on superposed, boosted (velocity ) solutions of single black
holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes
are considered. The excised regions containing the singularities are specified
by following the dynamics of apparent horizons. Evolutions of up to are obtained in which two initially separate apparent horizons are present
for . At that time a single enveloping apparent horizon forms,
indicating that the holes have merged. Apparent horizon area estimates suggest
gravitational radiation of about 2.6% of the total mass. The evolutions end
after a moderate amount of time because of instabilities.Comment: 2 References corrected, reference to figure update
Finding apparent horizons and other two-surfaces of constant expansion
Apparent horizons are structures of spacelike hypersurfaces that can be
determined locally in time. Closed surfaces of constant expansion (CE surfaces)
are a generalisation of apparent horizons. I present an efficient method for
locating CE surfaces. This method uses an explicit representation of the
surface, allowing for arbitrary resolutions and, in principle, shapes. The CE
surface equation is then solved as a nonlinear elliptic equation.
It is reasonable to assume that CE surfaces foliate a spacelike hypersurface
outside of some interior region, thus defining an invariant (but still
slicing-dependent) radial coordinate. This can be used to determine gauge modes
and to compare time evolutions with different gauge conditions. CE surfaces
also provide an efficient way to find new apparent horizons as they appear e.g.
in binary black hole simulations.Comment: 21 pages, 8 figures; two references adde
Accurate evolutions of unequal-mass neutron-star binaries: properties of the torus and short GRB engines
We present new results from accurate and fully general-relativistic
simulations of the coalescence of unmagnetized binary neutron stars with
various mass ratios. The evolution of the stars is followed through the
inspiral phase, the merger and prompt collapse to a black hole, up until the
appearance of a thick accretion disk, which is studied as it enters and remains
in a regime of quasi-steady accretion. Although a simple ideal-fluid equation
of state with \Gamma=2 is used, this work presents a systematic study within a
fully general relativistic framework of the properties of the resulting
black-hole--torus system produced by the merger of unequal-mass binaries. More
specifically, we show that: (1) The mass of the torus increases considerably
with the mass asymmetry and equal-mass binaries do not produce significant tori
if they have a total baryonic mass M_tot >~ 3.7 M_sun; (2) Tori with masses
M_tor ~ 0.2 M_sun are measured for binaries with M_tot ~ 3.4 M_sun and mass
ratios q ~ 0.75-0.85; (3) The mass of the torus can be estimated by the simple
expression M_tor(q, M_tot) = [c_1 (1-q) + c_2](M_max-M_tot), involving the
maximum mass for the binaries and coefficients constrained from the
simulations, and suggesting that the tori can have masses as large as M_tor ~
0.35 M_sun for M_tot ~ 2.8 M_sun and q ~ 0.75-0.85; (4) Using a novel technique
to analyze the evolution of the tori we find no evidence for the onset of
non-axisymmetric instabilities and that very little, if any, of their mass is
unbound; (5) Finally, for all the binaries considered we compute the complete
gravitational waveforms and the recoils imparted to the black holes, discussing
the prospects of detection of these sources for a number of present and future
detectors.Comment: 35 pages; small changes to match the published versio
Revisiting Event Horizon Finders
Event horizons are the defining physical features of black hole spacetimes,
and are of considerable interest in studying black hole dynamics. Here, we
reconsider three techniques to localise event horizons in numerical spacetimes:
integrating geodesics, integrating a surface, and integrating a level-set of
surfaces over a volume. We implement the first two techniques and find that
straightforward integration of geodesics backward in time to be most robust. We
find that the exponential rate of approach of a null surface towards the event
horizon of a spinning black hole equals the surface gravity of the black hole.
In head-on mergers we are able to track quasi-normal ringing of the merged
black hole through seven oscillations, covering a dynamic range of about 10^5.
Both at late times (when the final black hole has settled down) and at early
times (before the merger), the apparent horizon is found to be an excellent
approximation of the event horizon. In the head-on binary black hole merger,
only {\em some} of the future null generators of the horizon are found to start
from past null infinity; the others approach the event horizons of the
individual black holes at times far before merger.Comment: 30 pages, 15 figures, revision
Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes
We introduce a formulation of Eulerian general relativistic hydrodynamics
which is applicable for (perfect) fluid data prescribed on either spacelike or
null hypersurfaces. Simple explicit expressions for the characteristic speeds
and fields are derived in the general case. A complete implementation of the
formalism is developed in the case of spherical symmetry. The algorithm is
tested in a number of different situations, predisposing for a range of
possible applications. We consider the Riemann problem for a polytropic gas,
with initial data given on a retarded/advanced time slice of Minkowski
spacetime. We compute perfect fluid accretion onto a Schwarzschild black hole
spacetime using ingoing null Eddington-Finkelstein coordinates. Tests of fluid
evolution on dynamic background include constant density and TOV stars sliced
along the radial null cones. Finally, we consider the accretion of
self-gravitating matter onto a central black hole and the ensuing increase in
the mass of the black hole horizon.Comment: 23 pages, 13 figures, submitted to Phys. Rev.
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