443 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
Radiative falloff in the background of rotating black hole
We study numerically the late-time tails of linearized fields with any spin
in the background of a spinning black hole. Our code is based on the
ingoing Kerr coordinates, which allow us to penetrate through the event
horizon. The late time tails are dominated by the mode with the least multipole
moment which is consistent with the equatorial symmetry of the initial
data and is equal to or greater than the least radiative mode with and the
azimuthal number .Comment: 5 pages, 4 Encapsulated PostScript figures; Accepted to Phys. Rev. D
(Rapid Communication
Radiative falloff in Einstein-Straus spacetime
The Einstein-Straus spacetime describes a nonrotating black hole immersed in
a matter-dominated cosmology. It is constructed by scooping out a spherical
ball of the dust and replacing it with a vacuum region containing a black hole
of the same mass. The metric is smooth at the boundary, which is comoving with
the rest of the universe. We study the evolution of a massless scalar field in
the Einstein-Straus spacetime, with a special emphasis on its late-time
behavior. This is done by numerically integrating the scalar wave equation in a
double-null coordinate system that covers both portions (vacuum and dust) of
the spacetime. We show that the field's evolution is governed mostly by the
strong concentration of curvature near the black hole, and the discontinuity in
the dust's mass density at the boundary; these give rise to a rather complex
behavior at late times. Contrary to what it would do in an asymptotically-flat
spacetime, the field does not decay in time according to an inverse power-law.Comment: ReVTeX, 12 pages, 14 figure
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
Initial data for a head on collision of two Kerr-like black holes with close limit
We prove the existence of a family of initial data for the Einstein vacuum
equation which can be interpreted as the data for two Kerr-like black holes in
arbitrary location and with spin in arbitrary direction. This family of initial
data has the following properties: (i) When the mass parameter of one of them
is zero or when the distance between them goes to infinity, it reduces exactly
to the Kerr initial data. (ii) When the distance between them is zero, we
obtain exactly a Kerr initial data with mass and angular momentum equal to the
sum of the mass and angular momentum parameters of each of them. The initial
data depends smoothly on the distance, the mass and the angular momentum
parameters.Comment: 15 pages, no figures, Latex2
Radiative Tail of Realistic Rotating Gravitational Collapse
An astrophysically realistic model of wave dynamics in black-hole spacetimes
must involve a non-spherical background geometry with angular momentum. We
consider the evolution of gravitational (and electromagnetic) perturbations in
rotating Kerr spacetimes. We show that a rotating Kerr black hole becomes
`bald' slower than the corresponding spherically-symmetric Schwarzschild black
hole. Moreover, our results turn over the traditional belief (which has been
widely accepted during the last three decades) that the late-time tail of
gravitational collapse is universal. In particular, we show that different
fields have different decaying rates. Our results are also of importance both
to the study of the no-hair conjecture and the mass-inflation scenario
(stability of Cauchy horizons).Comment: 11 page
Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations
We consider the late-time evolution of {\it gravitational} and
electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We
give a detailed analysis of the mode-coupling phenomena in rotating
gravitational collapse. A consequence of this phenomena is that the late-time
tail is dominated by modes which, in general, may have an angular distribution
different from the original one. In addition, we show that different types of
fields have {\it different} decaying rates. This result turns over the
traditional belief (which has been widely accepted during the last three
decades) that the late-time tail of gravitational collapse is universal.Comment: 16 page
Second order gauge invariant gravitational perturbations of a Kerr black hole
We investigate higher than the first order gravitational perturbations in the
Newman-Penrose formalism. Equations for the Weyl scalar representing
outgoing gravitational radiation, can be uncoupled into a single wave equation
to any perturbative order. For second order perturbations about a Kerr black
hole, we prove the existence of a first and second order gauge (coordinates)
and tetrad invariant waveform, , by explicit construction. This
waveform is formed by the second order piece of plus a term, quadratic
in first order perturbations, chosen to make totally invariant and to
have the appropriate behavior in an asymptotically flat gauge.
fulfills a single wave equation of the form where is the same wave operator as for first order perturbations and is a
source term build up out of (known to this level) first order perturbations. We
discuss the issues of imposition of initial data to this equation, computation
of the energy and momentum radiated and wave extraction for direct comparison
with full numerical approaches to solve Einstein equations.Comment: 19 pages, REVTEX. Some misprints corrected and changes to improve
presentation. Version to appear in PR
Radiation tails and boundary conditions for black hole evolutions
In numerical computations of Einstein's equations for black hole spacetimes,
it will be necessary to use approximate boundary conditions at a finite
distance from the holes. We point out here that ``tails,'' the inverse
power-law decrease of late-time fields, cannot be expected for such
computations. We present computational demonstrations and discussions of
features of late-time behavior in an evolution with a boundary condition.Comment: submitted to Phys. Rev.
Late-time evolution of nonlinear gravitational collapse
We study numerically the fully nonlinear gravitational collapse of a
self-gravitating, minimally-coupled, massless scalar field in spherical
symmetry. Our numerical code is based on double-null coordinates and on free
evolution of the metric functions: The evolution equations are integrated
numerically, whereas the constraint equations are only monitored. The numerical
code is stable (unlike recent claims) and second-order accurate. We use this
code to study the late-time asymptotic behavior at fixed (outside the black
hole), along the event horizon, and along future null infinity. In all three
asymptotic regions we find that, after the decay of the quasi-normal modes, the
perturbations are dominated by inverse power-law tails. The corresponding power
indices agree with the integer values predicted by linearized theory. We also
study the case of a charged black hole nonlinearly perturbed by a (neutral)
self-gravitating scalar field, and find the same type of behavior---i.e.,
quasi-normal modes followed by inverse power-law tails, with the same indices
as in the uncharged case.Comment: 14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new
convergence test and a determination of QN ringing were added, in addition to
correction of typos and update of reference
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