332 research outputs found

### The Frenet Serret Description of Gyroscopic Precession

The phenomenon of gyroscopic precession is studied within the framework of
Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to
the congruence vorticity is highlighted with particular reference to the
irrotational congruence admitted by the stationary, axisymmetric spacetime.
General precession formulae are obtained for circular orbits with arbitrary
constant angular speeds. By successive reduction, different types of
precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime
family. The phenomenon is studied in the case of other interesting spacetimes,
such as the De Sitter and G\"{o}del universes as well as the general
stationary, cylindrical, vacuum spacetimes.Comment: 37 pages, Paper in Late

### R-mode Instability of Slowly Rotating Non-isentropic Relativistic Stars

We investigate properties of $r$-mode instability in slowly rotating
relativistic polytropes. Inside the star slow rotation and low frequency
formalism that was mainly developed by Kojima is employed to study axial
oscillations restored by Coriolis force. At the stellar surface, in order to
take account of gravitational radiation reaction effect, we use a near-zone
boundary condition instead of the usually imposed boundary condition for
asymptotically flat spacetime. Due to the boundary condition, complex
frequencies whose imaginary part represents secular instability are obtained
for discrete $r$-mode oscillations in some polytropic models. It is found that
such discrete $r$-mode solutions can be obtained only for some restricted
polytropic models. Basic properties of the solutions are similar to those
obtained by imposing the boundary condition for asymptotically flat spacetime.
Our results suggest that existence of a continuous part of spectrum cannot be
avoided even when its frequency becomes complex due to the emission of
gravitational radiation.Comment: 10 pages, 4 figures, accepted for publlication in PR

### Multipole particle in relativity

We discuss the motion of extended objects in a spacetime by considering a
gravitational field created by these objects. We define multipole moments of
the objects as a classification by Lie group SO(3). Then, we construct an
energy-momentum tensor for the objects and derive equations of motion from it.
As a result, we reproduce the Papapetrou equations for a spinning particle.
Furthermore, we will show that we can obtain more simple equations than the
Papapetrou equations by changing the center-of-mass.Comment: 22 pages, 2 figures. Accepted for publication in Phys. Rev.

### Relic Gravitational Waves and Their Detection

The range of expected amplitudes and spectral slopes of relic (squeezed)
gravitational waves, predicted by theory and partially supported by
observations, is within the reach of sensitive gravity-wave detectors. In the
most favorable case, the detection of relic gravitational waves can be achieved
by the cross-correlation of outputs of the initial laser interferometers in
LIGO, VIRGO, GEO600. In the more realistic case, the sensitivity of advanced
ground-based and space-based laser interferometers will be needed. The specific
statistical signature of relic gravitational waves, associated with the
phenomenon of squeezing, is a potential reserve for further improvement of the
signal to noise ratio.Comment: 25 pages, 9 figures included, revtex. Based on a talk given at
"Gyros, Clocks, and Interferometers: Testing General Relativity in Space"
(Germany, August 99

### Cold Plasma Dispersion Relations in the Vicinity of a Schwarzschild Black Hole Horizon

We apply the ADM 3+1 formalism to derive the general relativistic
magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild
metric. Respective perturbed equations are linearized for non-magnetized and
magnetized plasmas both in non-rotating and rotating backgrounds. These are
then Fourier analyzed and the corresponding dispersion relations are obtained.
These relations are discussed for the existence of waves with positive angular
frequency in the region near the horizon. Our results support the fact that no
information can be extracted from the Schwarzschild black hole. It is concluded
that negative phase velocity propagates in the rotating background whether the
black hole is rotating or non-rotating.Comment: 27 pages, 11 figures accepted for publication in Gen. Relat. & Gravi

### Boundary sources in the Doran - Lobo - Crawford spacetime

We take a null hypersurface (the causal horizon) generated by a congruence of
null geodesics as the boundary of the Doran-Lobo-Crawford spacetime, to be the
place where the Brown-York quasilocal energy is located. The components of the
outer and inner stress tensors are computed and shown to depend on time and on
the impact parameter $b$ of the test particle trajectory. The surface energy
density $\sigma$ on the boundary is given by the same expression as that
obtained previously for the energy stored on a Rindler horizon.Comment: 4 pages, title changed, no figures, minor text change

### Anomalous Hydrodynamics

Our goal is to examine the role of anomalies in the hydrodynamic regime of
field theories. We employ methods based on gauge/gravity duality to examine
R-charge anomalies in the hydrodynamic regime of stronly t'Hooft coupled, large
N, N = 4 Super Yang-Mills. We use a single particle spectrum treatment based on
the familiar "level crossing" picture of chiral anomalies to investigate
thermalized, massless QED. In each case, we work in the presence of a
homogeneous background magnetic field, and find the same result. Regardless of
whether a paricular current is anomalously non-conserved or not, as long as it
participates in an anomalous 3-pt. correlator, its constitutive relation
recieves a new term, proportional to a product of the anomaly coefficient, the
magnetic field, and any charge density participating in the anomaly. This
agrees with results found by Alekseev et.al. for QED. We include a general,
symmetry based argument for the presence of such terms, and use linear response
theory to determine their coefficients in a model with anomalous global
charges. This last method we apply to briefly examine baryon transport in
chiral QCD in a strong magnetic field.Comment: 23 pages, 2 figures. To be submitted to JHE

### Filtering post-Newtonian gravitational waves from coalescing binaries

Gravitational waves from inspiralling binaries are expected to be detected
using a data analysis technique known as {\it matched filtering.} This
technique is applicable whenever the form of the signal is known accurately.
Though we know the form of the signal precisely, we will not know {\it a
priori} its parameters. Hence it is essential to filter the raw output through
a host of search templates each corresponding to different values of the
parameters. The number of search templates needed in detecting the Newtonian
waveform characterized by three independent parameters is itself several
thousands. With the inclusion of post-Newtonian corrections the inspiral
waveform will have four independent parameters and this, it was thought, would
lead to an increase in the number of filters by several orders of
magnitude---an unfavorable feature since it would drastically slow down data
analysis. In this paper I show that by a judicious choice of signal parameters
we can work, even when the first post-Newtonian corrections are included, with
as many number of parameters as in the Newtonian case. In other words I
demonstrate that the effective dimensionality of the signal parameter space
does not change when first post-Newtonian corrections are taken into account.Comment: 5 pages, revtex, 2 figures available upon reques

### Stable Magnetic Universes Revisited

A regular class of static, cylindrically symmetric pure magnetic field
metrics is rederived in a different metric ansatz in all dimensions. Radial,
time dependent perturbations show that for dimensions d>3 such spacetimes are
stable at both near r\approx0 and large radius r\rightarrow\infty. In a
different gauge these stability analysis and similar results were known
beforehand. For d=3, however, simultaneous stability requirement at both, near
and far radial distances can not be reconciled for time - dependent
perturbations. Restricted, numerical geodesics for neutral particles reveal a
confinement around the center in the polar plane. Charged, time-like geodesics
for d=4 on the other hand are shown numerically to run toward infinity.Comment: 11 pages, 3figure

### Motion and gravitational radiation of a binary system consisting of an oscillating and rotating coplanar dusty disk and a point-like object

A binary system composed of an oscillating and rotating coplanar dusty disk
and a point mass is considered. The conservative dynamics is treated on the
Newtonian level. The effects of gravitational radiation reaction and wave
emission are studied to leading quadrupole order. The related waveforms are
given. The dynamical evolution of the system is determined semi-analytically
exploiting the Hamiltonian equations of motion which comprise the effects both
of the Newtonian tidal interaction and the radiation reaction on the motion of
the binary system in elliptic orbits. Tidal resonance effects between orbital
and oscillatory motions are considered in the presence of radiation damping.Comment: 26 pages, 8 figure

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