690 research outputs found
Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
I study the Bona-Masso family of hyperbolic slicing conditions, considering
in particular its properties when approaching two different types of
singularities: focusing singularities and gauge shocks. For focusing
singularities, I extend the original analysis of Bona et. al and show that both
marginal and strong singularity avoidance can be obtained for certain types of
behavior of the slicing condition as the lapse approaches zero. For the case of
gauge shocks, I re-derive a condition found previously that eliminates them.
Unfortunately, such a condition limits considerably the type of slicings
allowed. However, useful slicing conditions can still be found if one asks for
this condition to be satisfied only approximately. Such less restrictive
conditions include a particular member of the 1+log family, which in the past
has been found empirically to be extremely robust for both Brill wave and black
hole simulations.Comment: 11 pages, revtex4. Change in acknowledgment
Gravitational waves from extreme mass-ratio inspirals in Dynamical Chern-Simons gravity
Dynamical Chern-Simons gravity is an interesting extension of General
Relativity, which finds its way in many different contexts, including string
theory, cosmological settings and loop quantum gravity. In this theory, the
gravitational field is coupled to a scalar field by a parity-violating term,
which gives rise to characteristic signatures. Here we investigate how
Chern-Simons gravity would affect the quasi-circular inspiralling of a small,
stellar-mass object into a large non-rotating supermassive black hole, and the
accompanying emission of gravitational and scalar waves. We find the relevant
equations describing the perturbation induced by the small object, and we solve
them through the use of Green's function techniques. Our results show that for
a wide range of coupling parameters, the Chern-Simons coupling gives rise to an
increase in total energy flux, which translates into a fewer number of
gravitational-wave cycles over a certain bandwidth. For space-based
gravitational-wave detectors such as LISA, this effect can be used to constrain
the coupling parameter effectively.Comment: RevTex4, 18 pages, 7 figures, 1 tabl
Towards a Singularity-Proof Scheme in Numerical Relativity
Progress in numerical relativity has been hindered for 30 years because of
the difficulties of avoiding spacetime singularities in numerical evolution. We
propose a scheme which excises a region inside an apparent horizon containing
the singularity. Two major ingredients of the scheme are the use of a
horizon-locking coordinate and a finite differencing which respects the causal
structure of the spacetime. Encouraging results of the scheme in the spherical
collapse case are given.Comment: 9 page
Generic Tracking of Multiple Apparent Horizons with Level Flow
We report the development of the first apparent horizon locator capable of
finding multiple apparent horizons in a ``generic'' numerical black hole
spacetime. We use a level-flow method which, starting from a single arbitrary
initial trial surface, can undergo topology changes as it flows towards
disjoint apparent horizons if they are present. The level flow method has two
advantages: 1) The solution is independent of changes in the initial guess and
2) The solution can have multiple components. We illustrate our method of
locating apparent horizons by tracking horizon components in a short
Kerr-Schild binary black hole grazing collision.Comment: 13 pages including figures, submitted to Phys Rev
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
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
Black Hole--Scalar Field Interactions in Spherical Symmetry
We examine the interactions of a black hole with a massless scalar field
using a coordinate system which extends ingoing Eddington-Finkelstein
coordinates to dynamic spherically symmetric-spacetimes. We avoid problems with
the singularity by excising the region of the black hole interior to the
apparent horizon. We use a second-order finite difference scheme to solve the
equations. The resulting program is stable and convergent and will run forever
without problems. We are able to observe quasi-normal ringing and power-law
tails as well an interesting nonlinear feature.Comment: 16 pages, 26 figures, RevTex, to appear in Phys. Rev.
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
Are moving punctures equivalent to moving black holes?
When simulating the inspiral and coalescence of a binary black-hole system,
special care needs to be taken in handling the singularities. Two main
techniques are used in numerical-relativity simulations: A first and more
traditional one ``excises'' a spatial neighbourhood of the singularity from the
numerical grid on each spacelike hypersurface. A second and more recent one,
instead, begins with a ``puncture'' solution and then evolves the full
3-metric, including the singular point. In the continuum limit, excision is
justified by the light-cone structure of the Einstein equations and, in
practice, can give accurate numerical solutions when suitable discretizations
are used. However, because the field variables are non-differentiable at the
puncture, there is no proof that the moving-punctures technique is correct,
particularly in the discrete case. To investigate this question we use both
techniques to evolve a binary system of equal-mass non-spinning black holes. We
compare the evolution of two curvature 4-scalars with proper time along the
invariantly-defined worldline midway between the two black holes, using
Richardson extrapolation to reduce the influence of finite-difference
truncation errors. We find that the excision and moving-punctures evolutions
produce the same invariants along that worldline, and thus the same spacetimes
throughout that worldline's causal past. This provides convincing evidence that
moving-punctures are indeed equivalent to moving black holes.Comment: 4 pages, 3 eps color figures; v2 = major revisions to introduction &
conclusions based on referee comments, but no change in analysis or result
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