326 research outputs found
Formation of a rotating hole from a close limit head-on collision
Realistic black hole collisions result in a rapidly rotating Kerr hole, but
simulations to date have focused on nonrotating final holes. Using a new
solution of the Einstein initial value equations we present here waveforms and
radiation for an axisymmetric Kerr-hole-forming collision starting from small
initial separation (the ``close limit'' approximation) of two identical
rotating holes. Several new features are present in the results: (i) In the
limit of small separation, the waveform is linear (not quadratic) in the
separation. (ii) The waveforms show damped oscillations mixing quasinormal
ringing of different multipoles.Comment: 4 pages, 4 figures, submitted to PR
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Dynamic Games and Applications: Second Special Issue on Population Games: Introduction
Late-Time Evolution of Realistic Rotating Collapse and The No-Hair Theorem
We study analytically the asymptotic late-time evolution of realistic
rotating collapse. This is done by considering the asymptotic late-time
solutions of Teukolsky's master equation, which governs the evolution of
gravitational, electromagnetic, neutrino and scalar perturbations fields on
Kerr spacetimes. In accordance with the no-hair conjecture for rotating
black-holes we show that the asymptotic solutions develop inverse power-law
tails at the asymptotic regions of timelike infinity, null infinity and along
the black-hole outer horizon (where the power-law behaviour is multiplied by an
oscillatory term caused by the dragging of reference frames). The damping
exponents characterizing the asymptotic solutions at timelike infinity and
along the black-hole outer horizon are independent of the spin parameter of the
fields. However, the damping exponents at future null infinity are spin
dependent. The late-time tails at all the three asymptotic regions are
spatially dependent on the spin parameter of the field. The rotational dragging
of reference frames, caused by the rotation of the black-hole (or star) leads
to an active coupling of different multipoles.Comment: 16 page
Stability study of a model for the Klein-Gordon equation in Kerr spacetime
The current early stage in the investigation of the stability of the Kerr
metric is characterized by the study of appropriate model problems.
Particularly interesting is the problem of the stability of the solutions of
the Klein-Gordon equation, describing the propagation of a scalar field of mass
in the background of a rotating black hole. Rigorous results proof the
stability of the reduced, by separation in the azimuth angle in Boyer-Lindquist
coordinates, field for sufficiently large masses. Some, but not all, numerical
investigations find instability of the reduced field for rotational parameters
extremely close to 1. Among others, the paper derives a model problem for
the equation which supports the instability of the field down to .Comment: Updated version, after minor change
Radiative falloff in Schwarzschild-de Sitter spacetime
We consider the time evolution of a scalar field propagating in
Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it
were in pure Schwarzschild spacetime; the structure of spacetime far from the
black hole has no influence on the evolution. In this early epoch, the field's
initial outburst is followed by quasi-normal oscillations, and then by an
inverse power-law decay. At intermediate times, the power-law behavior gives
way to a faster, exponential decay. At late times, the field behaves as if it
were in pure de Sitter spacetime; the structure of spacetime near the black
hole no longer influences the evolution in a significant way. In this late
epoch, the field's behavior depends on the value of the curvature-coupling
constant xi. If xi is less than a critical value 3/16, the field decays
exponentially, with a decay constant that increases with increasing xi. If xi >
3/16, the field oscillates with a frequency that increases with increasing xi;
the amplitude of the field still decays exponentially, but the decay constant
is independent of xi.Comment: 10 pages, ReVTeX, 5 figures, references updated, and new section
adde
Relativistic Hydrodynamics around Black Holes and Horizon Adapted Coordinate Systems
Despite the fact that the Schwarzschild and Kerr solutions for the Einstein
equations, when written in standard Schwarzschild and Boyer-Lindquist
coordinates, present coordinate singularities, all numerical studies of
accretion flows onto collapsed objects have been widely using them over the
years. This approach introduces conceptual and practical complications in
places where a smooth solution should be guaranteed, i.e., at the gravitational
radius. In the present paper, we propose an alternative way of solving the
general relativistic hydrodynamic equations in background (fixed) black hole
spacetimes. We identify classes of coordinates in which the (possibly rotating)
black hole metric is free of coordinate singularities at the horizon,
independent of time, and admits a spacelike decomposition. In the spherically
symmetric, non-rotating case, we re-derive exact solutions for dust and perfect
fluid accretion in Eddington-Finkelstein coordinates, and compare with
numerical hydrodynamic integrations. We perform representative axisymmetric
computations. These demonstrations suggest that the use of those coordinate
systems carries significant improvements over the standard approach, especially
for higher dimensional studies.Comment: 10 pages, 4 postscript figures, accepted for publication in Phys.
Rev.
The imposition of Cauchy data to the Teukolsky equation II: Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations
We revisit the question of the imposition of initial data representing
astrophysical gravitational perturbations of black holes. We study their
dynamics for the case of nonrotating black holes by numerically evolving the
Teukolsky equation in the time domain. In order to express the Teukolsky
function Psi explicitly in terms of hypersurface quantities, we relate it to
the Moncrief waveform phi_M through a Chandrasekhar transformation in the case
of a nonrotating black hole. This relation between Psi and phi_M holds for any
constant time hypersurface and allows us to compare the computation of the
evolution of Schwarzschild perturbations by the Teukolsky and by the Zerilli
and Regge-Wheeler equations. We explicitly perform this comparison for the
Misner initial data in the close limit approach. We evolve numerically both,
the Teukolsky (with the recent code of Ref. [1]) and the Zerilli equations,
finding complete agreement in resulting waveforms within numerical error. The
consistency of these results further supports the correctness of the numerical
code for evolving the Teukolsky equation as well as the analytic expressions
for Psi in terms only of the three-metric and the extrinsic curvature.Comment: 14 pages, 7 Postscript figures, to appear in Phys. Rev.
Matter flows around black holes and gravitational radiation
We develop and calibrate a new method for estimating the gravitational
radiation emitted by complex motions of matter sources in the vicinity of black
holes. We compute numerically the linearized curvature perturbations induced by
matter fields evolving in fixed black hole backgrounds, whose evolution we
obtain using the equations of relativistic hydrodynamics. The current
implementation of the proposal concerns non-rotating holes and axisymmetric
hydrodynamical motions. As first applications we study i) dust shells falling
onto the black hole isotropically from finite distance, ii) initially spherical
layers of material falling onto a moving black hole, and iii) anisotropic
collapse of shells. We focus on the dependence of the total gravitational wave
energy emission on the flow parameters, in particular shell thickness, velocity
and degree of anisotropy. The gradual excitation of the black hole quasi-normal
mode frequency by sufficiently compact shells is demonstrated and discussed. A
new prescription for generating physically reasonable initial data is
discussed, along with a range of technical issues relevant to numerical
relativity.Comment: 27 pages, 12 encapsulated figures, revtex, amsfonts, submitted to
Phys. Rev.
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
Intermediate behavior of Kerr tails
The numerical investigation of wave propagation in the asymptotic domain of
Kerr spacetime has only recently been possible thanks to the construction of
suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle
in the decay rates of scalar fields: the late-time rates seemed to depend on
whether finite distance observers are in the strong field domain or far away
from the rotating black hole, an apparent phenomenon dubbed "splitting". We
discuss far-field "splitting" in the full field and near-horizon "splitting" in
certain projected modes using horizon-penetrating, hyperboloidal coordinates.
For either case we propose an explanation to the cause of the "splitting"
behavior, and we determine uniquely decay rates that previous studies found to
be ambiguous or immeasurable. The far-field "splitting" is explained by
competition between projected modes. The near-horizon "splitting" is due to
excitation of lower multipole modes that back excite the multipole mode for
which "splitting" is observed. In both cases "splitting" is an intermediate
effect, such that asymptotically in time strong field rates are valid at all
finite distances. At any finite time, however, there are three domains with
different decay rates whose boundaries move outwards during evolution. We then
propose a formula for the decay rate of tails that takes into account the
inter--mode excitation effect that we study.Comment: 16 page
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