817 research outputs found
Evolution equations for slowly rotating stars
We present a hyperbolic formulation of the evolution equations describing
non-radial perturbations of slowly rotating relativistic stars in the
Regge--Wheeler gauge. We demonstrate the stability preperties of the new
evolution set of equations and compute the polar w-modes for slowly rotating
stars.Comment: 27 pages, 2 figure
Late Time Tail of Wave Propagation on Curved Spacetime
The late time behavior of waves propagating on a general curved spacetime is
studied. The late time tail is not necessarily an inverse power of time. Our
work extends, places in context, and provides understanding for the known
results for the Schwarzschild spacetime. Analytic and numerical results are in
excellent agreement.Comment: 11 pages, WUGRAV-94-1
Low Frequency Tilt Seismology with a Precision Ground Rotation Sensor
We describe measurements of the rotational component of teleseismic surface
waves using an inertial high-precision ground-rotation-sensor installed at the
LIGO Hanford Observatory (LHO). The sensor has a noise floor of 0.4 nrad at 50 mHz and a translational coupling of less than 1 rad/m
enabling translation-free measurement of small rotations. We present
observations of the rotational motion from Rayleigh waves of six teleseismic
events from varied locations and with magnitudes ranging from M6.7 to M7.9.
These events were used to estimate phase dispersion curves which shows
agreement with a similar analysis done with an array of three STS-2
seismometers also located at LHO
Physical interpretation of gauge invariant perturbations of spherically symmetric space-times
By calculating the Newman-Penrose Weyl tensor components of a perturbed
spherically symmetric space-time with respect to invariantly defined classes of
null tetrads, we give a physical interpretation, in terms of gravitational
radiation, of odd parity gauge invariant metric perturbations. We point out how
these gauge invariants may be used in setting boundary and/or initial
conditions in perturbation theory.Comment: 6 pages. To appear in PR
High-Order Contamination in the Tail of Gravitational Collapse
It is well known that the late-time behaviour of gravitational collapse is
{\it dominated} by an inverse power-law decaying tail. We calculate {\it
higher-order corrections} to this power-law behaviour in a spherically
symmetric gravitational collapse. The dominant ``contamination'' is shown to
die off at late times as . This decay rate is much {\it
slower} than has been considered so far. It implies, for instance, that an
`exact' (numerical) determination of the power index to within
requires extremely long integration times of order . We show that the
leading order fingerprint of the black-hole electric {\it charge} is of order
.Comment: 12 pages, 2 figure
Radiative Falloff in Neutron Star Spacetimes
We systematically study late-time tails of scalar waves propagating in
neutron star spacetimes. We consider uniform density neutron stars, for which
the background spacetime is analytic and the compaction of the star can be
varied continously between the Newtonian limit 2M/R << 1 and the relativistic
Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off
neutron stars of different compactions 2M/R and find that a Newtonian, an
intermediate, and a highly relativistic regime can be clearly distinguished. In
the highly relativistic regime, the reflected signal is dominated by
quasi-periodic peaks, which originate from the wave packet bouncing back and
forth between the center of the star and the maximum of the background
curvature potential at R ~ 3 M. Between these peaks, the field decays according
to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between
the center and the maximum or the curvature potential grows without bound, so
that the first peak arrives only at infinitely late time. The modes of neutron
stars can therefore no longer be excited in the ultra-relativistic limit, and
it is in this sense that the late-time radiative decay from neutron stars
looses all its features and gives rise to power-law tails reminiscent of
Schwarzschild black holes.Comment: 10 pages, 7 figures, to appear in PR
Covariant Perturbations of Schwarzschild Black Holes
We present a new covariant and gauge-invariant perturbation formalism for
dealing with spacetimes having spherical symmetry (or some preferred spatial
direction) in the background, and apply it to the case of gravitational wave
propagation in a Schwarzschild black hole spacetime. The 1+3 covariant approach
is extended to a `1+1+2 covariant sheet' formalism by introducing a radial unit
vector in addition to the timelike congruence, and decomposing all covariant
quantities with respect to this. The background Schwarzschild solution is
discussed and a covariant characterisation is given. We give the full
first-order system of linearised 1+1+2 covariant equations, and we show how, by
introducing (time and spherical) harmonic functions, these may be reduced to a
system of first-order ordinary differential equations and algebraic constraints
for the 1+1+2 variables which may be solved straightforwardly. We show how both
the odd and even parity perturbations may be unified by the discovery of a
covariant, frame- and gauge-invariant, transverse-traceless tensor describing
gravitational waves, which satisfies a covariant wave equation equivalent to
the Regge-Wheeler equation for both even and odd parity perturbations. We show
how the Zerilli equation may be derived from this tensor, and derive a similar
transverse traceless tensor equivalent to this equation. The so-called
`special' quasinormal modes with purely imaginary frequency emerge naturally.
The significance of the degrees of freedom in the choice of the two frame
vectors is discussed, and we demonstrate that, for a certain frame choice, the
underlying dynamics is governed purely by the Regge-Wheeler tensor. The two
transverse-traceless Weyl tensors which carry the curvature of gravitational
waves are discussed.Comment: 23 pages, 1 figure, Revtex 4. Submitted to Classical and Quantum
Gravity. Revised version is significantly streamlined with an important error
corrected which simplifies the presentatio
Late-Time Evolution of Charged Gravitational Collapse and Decay of Charged Scalar Hair - II
We study analytically the initial value problem for a charged massless
scalar-field on a Reissner-Nordstr\"om spacetime. Using the technique of
spectral decomposition we extend recent results on this problem. Following the
no-hair theorem we reveal the dynamical physical mechanism by which the charged
hair is radiated away. We show that the charged perturbations decay according
to an inverse power-law behaviour at future timelike infinity and along future
null infinity. Along the future outer horizon we find an oscillatory inverse
power-law relaxation of the charged fields. We find that a charged black hole
becomes ``bald'' slower than a neutral one, due to the existence of charged
perturbations. Our results are also important to the study of mass-inflation
and the stability of Cauchy horizons during a dynamical gravitational collapse
of charged matter in which a charged black-hole is formed.Comment: Latex 15 pages, Revtex.st
Late-time evolution of a self-interacting scalar field in the spacetime of dilaton black hole
We investigate the late-time tails of self-interacting (massive) scalar
fields in the spacetime of dilaton black hole. Following the no hair theorem we
examine the mechanism by which self-interacting scalar hair decay. We revealed
that the intermediate asymptotic behavior of the considered field perturbations
is dominated by an oscillatory inverse power-law decaying tail. The numerical
simulations showed that at the very late-time massive self-interacting scalar
hair decayed slower than any power law.Comment: 8 pages, 4 figures, to appear in Phys. Rev.
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