259 research outputs found
Perturbative evolution of the static configurations, quasinormal modes and quasi normal ringing in the Apostolatos - Thorne cylindrical shell model
We study the perturbative evolution of the static configurations, quasinormal
modes and quasi normal ringing in the Apostolatos - Thorne cylindrical shell
model. We consider first an expansion in harmonic modes and show that it
provides a complete solution for the characteristic value problem for the
finite perturbations of a static configuration. As a consequence of this
completeness we obtain a proof of the stability of static solutions under this
type of perturbations. The explicit expression for the mode expansion are then
used to obtain numerical values for some of the quasi normal mode complex
frequencies. Some examples involving the numerical evaluation of the integral
mode expansions are described and analyzed, and the quasi normal ringing
displayed by the solutions is found to be in agreement with quasi normal modes
found previously. Going back to the full relativistic equations of motion we
find their general linear form by expanding to first order about a static
solution. We then show that the resulting set of coupled ordinary and partial
differential equations for the dynamical variables of the system can be used to
set an initial plus boundary values problem, and prove that there is an
associated positive definite constant of the motion that puts absolute bounds
on the dynamic variables of the system, establishing the stability of the
motion of the shell under arbitrary, finite perturbations. We also show that
the problem can be solved numerically, and provide some explicit examples that
display the complete agreement between the purely numerical evolution and that
obtained using the mode expansion, in particular regarding the quasi normal
ringing that results in the evolution of the system. We also discuss the
relation of the present work to some recent results on the same model that have
appeared in the literature.Comment: 27 pages, 7 figure
Near-Extreme Black Holes and the Universal Relaxation Bound
A fundamental bound on the relaxation time \tau of a perturbed
thermodynamical system has recently been derived, \tau \geq \hbar/\pi T, where
is the system's temperature. We demonstrate analytically that black holes
saturate this bound in the extremal limit and for large values of the azimuthal
number m of the perturbation field.Comment: 2 Pages. Submitted to PRD on 5/12/200
Self lensing effects for compact stars and their mass-radius relation
During the last couple of years astronomers and astrophysicists have been
debating on the fact whether the so called `strange stars' - stars made up of
strange quark matter, have been discovered with the candidates like SAX
J1808.4-3658, 4U 1728-34, RX J1856.5-3754, etc. The main contention has been
the estimation of radius of the star for an assumed mass of ~ 1.4 M_sun and to
see whether the point overlaps with the graphs for the neutron star equation of
state or whether it goes to the region of stars made of strange matter equation
of state. Using the well established formulae from general relativity for the
gravitational redshift and the `lensing effect' due to bending of photon
trajectories, we, in this letter, relate the parameters M and R with the
observable parameters, the redshift z and the radiation radius R_\infty, thus
constraining both M and R for specific ranges, without any other arbitrariness.
With the required inputs from observations, one ought to incorporate the
effects of self lensing of the compact stars which has been otherwise ignored
in all of the estimations done so far. Nonetheless, these effect of self
lensing makes a marked difference and constraints on the M-R relation.Comment: 7 pages, 1 figure, accepted for publication in Mod. Phys. Lett.
On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
Newly formed black holes are expected to emit characteristic radiation in the
form of quasi-normal modes, called ringdown waves, with discrete frequencies.
LISA should be able to detect the ringdown waves emitted by oscillating
supermassive black holes throughout the observable Universe. We develop a
multi-mode formalism, applicable to any interferometric detectors, for
detecting ringdown signals, for estimating black hole parameters from those
signals, and for testing the no-hair theorem of general relativity. Focusing on
LISA, we use current models of its sensitivity to compute the expected
signal-to-noise ratio for ringdown events, the relative parameter estimation
accuracy, and the resolvability of different modes. We also discuss the extent
to which uncertainties on physical parameters, such as the black hole spin and
the energy emitted in each mode, will affect our ability to do black hole
spectroscopy.Comment: 44 pages, 21 figures, 10 tables. Minor changes to match version in
press in Phys. Rev.
Quasi-normal modes of Schwarzschild-de Sitter black holes
The low-laying frequencies of characteristic quasi-normal modes (QNM) of
Schwarzschild-de Sitter (SdS) black holes have been calculated for fields of
different spin using the 6th-order WKB approximation and the approximation by
the P\"{o}shl-Teller potential. The well-known asymptotic formula for large
is generalized here on a case of the Schwarzchild-de Sitter black hole. In the
limit of the near extreme term the results given by both methods are
in a very good agreement, and in this limit fields of different spin decay with
the same rate.Comment: 9 pages, 1 ancillary Mathematica(R) noteboo
Analytic structure of radiation boundary kernels for blackhole perturbations
Exact outer boundary conditions for gravitational perturbations of the
Schwarzschild metric feature integral convolution between a time-domain
boundary kernel and each radiative mode of the perturbation. For both axial
(Regge-Wheeler) and polar (Zerilli) perturbations, we study the Laplace
transform of such kernels as an analytic function of (dimensionless) Laplace
frequency. We present numerical evidence indicating that each such
frequency-domain boundary kernel admits a "sum-of-poles" representation. Our
work has been inspired by Alpert, Greengard, and Hagstrom's analysis of
nonreflecting boundary conditions for the ordinary scalar wave equation.Comment: revtex4, 14 pages, 12 figures, 3 table
Boundary conditions at spatial infinity for fields in Casimir calculations
The importance of imposing proper boundary conditions for fields at spatial
infinity in the Casimir calculations is elucidated.Comment: 8 pages, 1 figure, submitted to the Proceedings of The Seventh
Workshop QFEXT'05 (Barcelona, September 5-9, 2005
Quasinormal Modes, the Area Spectrum, and Black Hole Entropy
The results of canonical quantum gravity concerning geometric operators and
black hole entropy are beset by an ambiguity labelled by the Immirzi parameter.
We use a result from classical gravity concerning the quasinormal mode spectrum
of a black hole to fix this parameter in a new way. As a result we arrive at
the Bekenstein - Hawking expression of for the entropy of a black
hole and in addition see an indication that the appropriate gauge group of
quantum gravity is SO(3) and not its covering group SU(2).Comment: 4 pages, 2 figure
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