4,005 research outputs found
Perturbed Self-Similar Massless Scalar Field in Spherically Symmetric Spaceimes
In this paper, we investigate the linear perturbations of the spherically
symmetric spacetimes with kinematic self-similarity of the second kind. The
massless scalar field equations are solved which yield the background and an
exact solutions for the perturbed equations. We discuss the boundary conditions
of the resulting perturbed solutions. The possible perturbation modes turn out
to be stable as well as unstable. The analysis leads to the conclusion that
there does not exist any critical solution.Comment: 15 pages, accepted for publication Int. J. Mod. Phys.
Perturbative Analysis of Universality and Individuality in Gravitational Waves from Neutron Stars
The universality observed in gravitational wave spectra of non-rotating
neutron stars is analyzed here. We show that the universality in the axial
oscillation mode can be reproduced with a simple stellar model, namely the
centrifugal barrier approximation (CBA), which captures the essence of the
Tolman VII model of compact stars. Through the establishment of scaled
co-ordinate logarithmic perturbation theory (SCLPT), we are able to explain and
quantitatively predict such universal behavior. In addition, quasi-normal modes
of individual neutron stars characterized by different equations of state can
be obtained from those of CBA with SCLPT.Comment: 29 pages, 10 figures, submitted to Astrophysical Journa
Gravitational Radiation from a Naked Singularity -- Odd-Parity Perturbation --
It has been suggested that a naked singularity may be a good candidate for a
strong gravitational wave burster. The naked singularity occurs in the generic
collapse of an inhomogeneous dust ball. We study odd-parity mode of
gravitational waves from a naked singularity of the Lema\^{\i}tre-Tolman-Bondi
space-time. The wave equation for gravitational waves are solved by numerical
integration using the single null coordinate. The result is that the naked
singularity is not a strong source of the odd-parity gravitational radiation
although the metric perturbation grows in the central region. Therefore, the
Cauchy horizon in this space-time would be marginally stable against odd-parity
perturbations.Comment: 14 pages, 7 figures, to be published in Prog. Theor. Phys. Final
version, with minor changes. Reference 13 adde
On the Superradiance of Spin-1 Waves in an Equatorial Wedge around a Kerr Hole
Recently Van Putten has suggested that superradiance of magnetosonic waves in
a toroidal magnetosphere around a Kerr black hole may play a role in the
central engine of gamma-ray bursts. In this context, he computed (in the WKB
approximation) the superradiant amplification of scalar waves confined to a
thin equatorial wedge around a Kerr hole and found that the superradiance is
higher than for radiation incident over all angles. This paper presents
calculations of both spin-0 (scalar) superradiance (integrating the radial
equation rather than using the WKB method) and and spin-1
(electromagnetic/magnetosonic) superradiance, in Van Putten's wedge geometry.
In contrast to the scalar case, spin-1 superradiance decreases in the wedge
geometry, decreasing the likelihood of its astrophysical importance.Comment: Submitted to The Astrophysical Journal Letter
Transient Rayleigh-Benard-Marangoni Convection due to Evaporation : a Linear Non-normal Stability Analysis
The convective instability in a plane liquid layer with time-dependent
temperature profile is investigated by means of a general method suitable for
linear stability analysis of an unsteady basic flow. The method is based on a
non-normal approach, and predicts the onset of instability, critical wave
number and time. The method is applied to transient Rayleigh-Benard-Marangoni
convection due to cooling by evaporation. Numerical results as well as
theoretical scalings for the critical parameters as function of the Biot number
are presented for the limiting cases of purely buoyancy-driven and purely
surface-tension-driven convection. Critical parameters from calculations are in
good agreement with those from experiments on drying polymer solutions, where
the surface cooling is induced by solvent evaporation.Comment: 31 pages, 8 figure
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