85 research outputs found
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
On the linear stability of solitons and hairy black holes with a negative cosmological constant: the odd-parity sector
Using a recently developed perturbation formalism based on curvature
quantities, we investigate the linear stability of black holes and solitons
with Yang-Mills hair and a negative cosmological constant. We show that those
solutions which have no linear instabilities under odd- and even- parity
spherically symmetric perturbations remain stable under odd-parity, linear,
non-spherically symmetric perturbations.Comment: 26 pages, 1 figur
Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations
Many alternative formulations of Einstein's evolution have lately been
examined, in an effort to discover one which yields slow growth of
constraint-violating errors. In this paper, rather than directly search for
well-behaved formulations, we instead develop analytic tools to discover which
formulations are particularly ill-behaved. Specifically, we examine the growth
of approximate (geometric-optics) solutions, studied only in the future domain
of dependence of the initial data slice (e.g. we study transients). By
evaluating the amplification of transients a given formulation will produce, we
may therefore eliminate from consideration the most pathological formulations
(e.g. those with numerically-unacceptable amplification). This technique has
the potential to provide surprisingly tight constraints on the set of
formulations one can safely apply. To illustrate the application of these
techniques to practical examples, we apply our technique to the 2-parameter
family of evolution equations proposed by Kidder, Scheel, and Teukolsky,
focusing in particular on flat space (in Rindler coordinates) and Schwarzchild
(in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.
Improved outer boundary conditions for Einstein's field equations
In a recent article, we constructed a hierarchy B_L of outer boundary
conditions for Einstein's field equations with the property that, for a
spherical outer boundary, it is perfectly absorbing for linearized
gravitational radiation up to a given angular momentum number L. In this
article, we generalize B_2 so that it can be applied to fairly general
foliations of spacetime by space-like hypersurfaces and general outer boundary
shapes and further, we improve B_2 in two steps: (i) we give a local boundary
condition C_2 which is perfectly absorbing including first order contributions
in 2M/R of curvature corrections for quadrupolar waves (where M is the mass of
the spacetime and R is a typical radius of the outer boundary) and which
significantly reduces spurious reflections due to backscatter, and (ii) we give
a non-local boundary condition D_2 which is exact when first order corrections
in 2M/R for both curvature and backscatter are considered, for quadrupolar
radiation.Comment: accepted Class. Quant. Grav. numerical relativity special issue; 17
pages and 1 figur
Stability properties of black holes in self-gravitating nonlinear electrodynamics
We analyze the dynamical stability of black hole solutions in
self-gravitating nonlinear electrodynamics with respect to arbitrary linear
fluctuations of the metric and the electromagnetic field. In particular, we
derive simple conditions on the electromagnetic Lagrangian which imply linear
stability in the domain of outer communication. We show that these conditions
hold for several of the regular black hole solutions found by Ayon-Beato and
Garcia.Comment: 15 pages, no figure
Characterizing asymptotically anti-de Sitter black holes with abundant stable gauge field hair
In the light of the "no-hair" conjecture, we revisit stable black holes in
su(N) Einstein-Yang-Mills theory with a negative cosmological constant. These
black holes are endowed with copious amounts of gauge field hair, and we
address the question of whether these black holes can be uniquely characterized
by their mass and a set of global non-Abelian charges defined far from the
black hole. For the su(3) case, we present numerical evidence that stable black
hole configurations are fixed by their mass and two non-Abelian charges. For
general N, we argue that the mass and N-1 non-Abelian charges are sufficient to
characterize large stable black holes, in keeping with the spirit of the
"no-hair" conjecture, at least in the limit of very large magnitude
cosmological constant and for a subspace containing stable black holes (and
possibly some unstable ones as well).Comment: 33 pages, 13 figures, minor change
Numerical stability for finite difference approximations of Einstein's equations
We extend the notion of numerical stability of finite difference
approximations to include hyperbolic systems that are first order in time and
second order in space, such as those that appear in Numerical Relativity. By
analyzing the symbol of the second order system, we obtain necessary and
sufficient conditions for stability in a discrete norm containing one-sided
difference operators. We prove stability for certain toy models and the
linearized Nagy-Ortiz-Reula formulation of Einstein's equations.
We also find that, unlike in the fully first order case, standard
discretizations of some well-posed problems lead to unstable schemes and that
the Courant limits are not always simply related to the characteristic speeds
of the continuum problem. Finally, we propose methods for testing stability for
second order in space hyperbolic systems.Comment: 18 pages, 9 figure
Numerical simulations with a first order BSSN formulation of Einstein's field equations
We present a new fully first order strongly hyperbolic representation of the
BSSN formulation of Einstein's equations with optional constraint damping
terms. We describe the characteristic fields of the system, discuss its
hyperbolicity properties, and present two numerical implementations and
simulations: one using finite differences, adaptive mesh refinement and in
particular binary black holes, and another one using the discontinuous Galerkin
method in spherical symmetry. The results of this paper constitute a first step
in an effort to combine the robustness of BSSN evolutions with very high
accuracy numerical techniques, such as spectral collocation multi-domain or
discontinuous Galerkin methods.Comment: To appear in Physical Review
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