59 research outputs found
Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems
We present approximate analytical solutions to the Hamiltonian and momentum
constraint equations, corresponding to systems composed of two black holes with
arbitrary linear and angular momentum. The analytical nature of these initial
data solutions makes them easier to implement in numerical evolutions than the
traditional numerical approach of solving the elliptic equations derived from
the Einstein constraints. Although in general the problem of setting up initial
conditions for black hole binary simulations is complicated by the presence of
singularities, we show that the methods presented in this work provide initial
data with and norms of violation of the constraint equations
falling below those of the truncation error (residual error due to
discretization) present in finite difference codes for the range of grid
resolutions currently used. Thus, these data sets are suitable for use in
evolution codes. Detailed results are presented for the case of a head-on
collision of two equal-mass M black holes with specific angular momentum 0.5M
at an initial separation of 10M. A straightforward superposition method yields
data adequate for resolutions of , and an "attenuated" superposition
yields data usable to resolutions at least as fine as . In addition, the
attenuated approximate data may be more tractable in a full (computational)
exact solution to the initial value problem.Comment: 6 pages, 5 postscript figures. Minor changes and some points
clarified. Accepted for publication in Phys. Rev.
Area Invariance of Apparent Horizons under Arbitrary Boosts
It is a well known analytic result in general relativity that the
2-dimensional area of the apparent horizon of a black hole remains invariant
regardless of the motion of the observer, and in fact is independent of the slice, which can be quite arbitrary in general relativity.
Nonetheless the explicit computation of horizon area is often substantially
more difficult in some frames (complicated by the coordinate form of the
metric), than in other frames. Here we give an explicit demonstration for very
restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the
Kerr-Schild coordinate expression for these spacetimes they have an explicit
Lorentz-invariant form. We consider {\it boosted} versions with the black hole
moving through the coordinate system. Since these are stationary black hole
spacetimes, the apparent horizons are two dimensional cross sections of their
event horizons, so we compute the areas of apparent horizons in the boosted
space with (boosted) , and obtain the same result as in the
unboosted case. Note that while the invariance of area is generic, we deal only
with black holes in the Kerr-Schild form, and consider only one particularly
simple change of slicing which amounts to a boost. Even with these restrictions
we find that the results illuminate the physics of the horizon as a null
surface and provide a useful pedagogical tool. As far as we can determine, this
is the first explicit calculation of this type demonstrating the area
invariance of horizons. Further, these calculations are directly relevant to
transformations that arise in computational representation of moving black
holes. We present an application of this result to initial data for boosted
black holes.Comment: 19 pages, 3 figures. Added a new section and 2 plots along with a
coautho
Cosmic Superstring Scattering in Backgrounds
We generalize the calculation of cosmic superstring reconnection probability
to non-trivial backgrounds. This is done by modeling cosmic strings as wound
tachyon modes in the 0B theory, and the spacetime effective action is then used
to couple this to background fields. Simple examples are given including
trivial and warped compactifications. Generalization to strings is
discussed.Comment: 12 pages, 2 figures; v2: references adde
Close limit evolution of Kerr-Schild type initial data for binary black holes
We evolve the binary black hole initial data family proposed by Bishop {\em
et al.} in the limit in which the black holes are close to each other. We
present an exact solution of the linearized initial value problem based on
their proposal and make use of a recently introduced generalized formalism for
studying perturbations of Schwarzschild black holes in arbitrary coordinates to
perform the evolution. We clarify the meaning of the free parameters of the
initial data family through the results for the radiated energy and waveforms
from the black hole collision.Comment: 8 pages, RevTex, four eps figure
Tracking Black Holes in Numerical Relativity
This work addresses and solves the problem of generically tracking black hole
event horizons in computational simulation of black hole interactions.
Solutions of the hyperbolic eikonal equation, solved on a curved spacetime
manifold containing black hole sources, are employed in development of a robust
tracking method capable of continuously monitoring arbitrary changes of
topology in the event horizon, as well as arbitrary numbers of gravitational
sources. The method makes use of continuous families of level set viscosity
solutions of the eikonal equation with identification of the black hole event
horizon obtained by the signature feature of discontinuity formation in the
eikonal's solution. The method is employed in the analysis of the event horizon
for the asymmetric merger in a binary black hole system. In this first such
three dimensional analysis, we establish both qualitative and quantitative
physics for the asymmetric collision; including: 1. Bounds on the topology of
the throat connecting the holes following merger, 2. Time of merger, and 3.
Continuous accounting for the surface of section areas of the black hole
sources.Comment: 14 pages, 16 figure
D-Branes in Field Theory
Certain gauge theories in four dimensions are known to admit semi-classical
D-brane solitons. These are domain walls on which vortex flux tubes may end.
The purpose of this paper is to develop an open-string description of these
D-branes. The dynamics of the domain walls is shown to be governed by a
Chern-Simons-Higgs theory which, at the quantum level, captures the classical
"closed string" scattering of domain wall solitons.Comment: 23 Pages, 3 figures. v2: reference adde
Modeling the Radio and X-ray Emission of SN 1993J and SN 2002ap
Modeling of radio and X-ray observations of supernovae interacting with their
circumstellar media are discussed, with special application to SN 1993J and SN
2002ap. We emphasize the importance of including all relevant physical
mechanisms, especially for the modeling of the radio light curves. The
different conclusions for the absorption mechanism (free-free or synchrotron
self-absorption), as well as departures from an CSM, as
inferred by some authors, are discussed in detail. We conclude that the
evidence for a variation in the mass loss rate with time is very weak. The
results regarding the efficiencies of magnetic field generation and
relativistic particle acceleration are summarized.Comment: 10 pages, 2 figures. Uses svmult.cls. To appear in proceedings of IAU
Colloquium 192 "Supernovae (10 years of SN 1993J)", April 2003, Valencia,
Spain, eds. J. M. Marcaide and K. W. Weile
Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy
A generalized model of space-time is given, taking into consideration the
anisotropic structure of fields which are depended on the position and the
direction (velocity).In this framework a generalized FRW-metric the
Raychaudhouri and Friedmann equations are studied.A long range vector field of
cosmological origin is considered in relation to the physical geometry of
space-time in which Cartan connection has a fundamental role.The generalised
Friedmann equations are produced including anisotropic terms.The variation of
anisotropy is expressed in terms of the Cartan torsion tensor of the
Finslerian space-time.A possible estimation of the anisotropic parameter
can be achieved with the aid of the de-Sitter model of the empty flat universe
with weak anisotropy. Finally a physical generalisation for the model of
inflation is also studied.Comment: 21 pages- to appear in GR
New Black Hole Solutions in Brans-Dicke Theory of Gravity
Existence check of non-trivial, stationary axisymmetric black hole solutions
in Brans-Dicke theory of gravity in different direction from those of Penrose,
Thorne and Dykla, and Hawking is performed. Namely, working directly with the
known explicit spacetime solutions in Brans-Dicke theory, it is found that
non-trivial Kerr-Newman-type black hole solutions different from general
relativistic solutions could occur for the generic Brans-Dicke parameter values
-5/2\leq \omega <-3/2. Finally, issues like whether these new black holes carry
scalar hair and can really arise in nature and if they can, what the associated
physical implications would be are discussed carefully.Comment: 20 pages, no figure, Revtex, version to appear in Phys. Rev.
On Born approximation in black hole scattering
A massless field propagating on spherically symmetric black hole metrics such
as the Schwarzschild, Reissner-Nordstr\"{o}m and Reissner-Nordstr\"{o}m-de
Sitter backgrounds is considered. In particular, explicit formulae in terms of
transcendental functions for the scattering of massless scalar particles off
black holes are derived within a Born approximation. It is shown that the
conditions on the existence of the Born integral forbid a straightforward
extraction of the quasi normal modes using the Born approximation for the
scattering amplitude. Such a method has been used in literature. We suggest a
novel, well defined method, to extract the large imaginary part of quasinormal
modes via the Coulomb-like phase shift. Furthermore, we compare the numerically
evaluated exact scattering amplitude with the Born one to find that the
approximation is not very useful for the scattering of massless scalar,
electromagnetic as well as gravitational waves from black holes
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