185 research outputs found
Quantum cosmological perfect fluid model and its classical analogue
The quantization of gravity coupled to a perfect fluid model leads to a
Schr\"odinger-like equation, where the matter variable plays the role of time.
The wave function can be determined, in the flat case, for an arbitrary
barotropic equation of state ; solutions can also be found for
the radiative non-flat case. The wave packets are constructed, from which the
expectation value for the scale factor is determined. The quantum scenarios
reveal a bouncing Universe, free from singularity. We show that such quantum
cosmological perfect fluid models admit a universal classical analogue,
represented by the addition, to the ordinary classical model, of a repulsive
stiff matter fluid. The meaning of the existence of this universal classical
analogue is discussed. The quantum cosmological perfect fluid model is, for a
flat spatial section, formally equivalent to a free particle in ordinary
quantum mechanics, for any value of , while the radiative non-flat case
is equivalent to the harmonic oscillator. The repulsive fluid needed to
reproduce the quantum results is the same in both cases.Comment: Latex file, 13 page
Spherical Solutions due to the Exterior Geometry of a Charged Weyl Black Hole
Firstly we derive peculiar spherical Weyl solutions, using a general
spherically symmetric metric due to a massive charged object with definite mass
and radius. Afterwards, we present new analytical solutions for relevant
cosmological terms, which appear in the metrics. Connecting the metrics to a
new geometric definition of a charged Black Hole, we numerically investigate
the effective potentials of the total dynamical system, considering massive and
massless test particles, moving on such Black Holes.Comment: 8 pages, 5 figure
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
On Relativistic Material Reference Systems
This work closes certain gaps in the literature on material reference systems
in general relativity. It is shown that perfect fluids are a special case of
DeWitt's relativistic elastic media and that the velocity--potential formalism
for perfect fluids can be interpreted as describing a perfect fluid coupled to
a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is
carried out and the constraints that arise when the system is coupled to
gravity are studied. When the Hamiltonian constraint is resolved with respect
to the clock momentum, the resulting true Hamiltonian is found to be a
functional only of the gravitational variables. The true Hamiltonian is
explicitly displayed when the medium is dust, and is shown to depend on the
detailed construction of the clocks.Comment: 18 pages, ReVTe
The Stability of an Isentropic Model for a Gaseous Relativistic Star
We show that the isentropic subclass of Buchdahl's exact solution for a
gaseous relativistic star is stable and gravitationally bound for all values of
the compactness ratio , where is the total mass and is
the radius of the configuration in geometrized units] in the range, , corresponding to the {\em regular} behaviour of the solution. This
result is in agreement with the expectation and opposite to the earlier claim
found in the literature.Comment: 9 pages (including 1 table); accepted for publication in GR
Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion
A particle of mass moves on a circular orbit around a nonrotating black
hole of mass . Under the assumption the gravitational waves
emitted by such a binary system can be calculated exactly numerically using
black-hole perturbation theory. If, further, the particle is slowly moving,
then the waves can be calculated approximately analytically, and expressed in
the form of a post-Newtonian expansion. We determine the accuracy of this
expansion in a quantitative way by calculating the reduction in signal-to-noise
ratio incurred when matched filtering the exact signal with a nonoptimal,
post-Newtonian filter.Comment: 5 pages, ReVTeX, 1 figure. A typographical error was discovered in
the computer code used to generate the results presented in the paper. The
corrected results are presented in an Erratum, which also incorporates new
results, obtained using the recently improved post-Newtonian calculations of
Tanaka, Tagoshi, and Sasak
Results of the First Coincident Observations by Two Laser-Interferometric Gravitational Wave Detectors
We report an upper bound on the strain amplitude of gravitational wave bursts
in a waveband from around 800Hz to 1.25kHz. In an effective coincident
observing period of 62 hours, the prototype laser interferometric gravitational
wave detectors of the University of Glasgow and Max Planck Institute for
Quantum Optics, have set a limit of 4.9E-16, averaging over wave polarizations
and incident directions. This is roughly a factor of 2 worse than the
theoretical best limit that the detectors could have set, the excess being due
to unmodelled non-Gaussian noise. The experiment has demonstrated the viability
of the kind of observations planned for the large-scale interferometers that
should be on-line in a few years time.Comment: 11 pages, 2 postscript figure
Nonlinear Gravitational Waves: Their Form and Effects
A gravitational wave must be nonlinear to be able to transport its own
source, that is, energy and momentum. A physical gravitational wave, therefore,
cannot be represented by a solution to a linear wave equation. Relying on this
property, the second-order solution describing such physical waves is obtained.
The effects they produce on free particles are found to consist of nonlinear
oscillations along the direction of propagation.Comment: 15 pages, no figures. v2: presentation changes aiming at clarifying
the text; matches published versio
Gravitational waves from inspiralling compact binaries: Parameter estimation using second-post-Newtonian waveforms
The parameters of inspiralling compact binaries can be estimated using
matched filtering of gravitational-waveform templates against the output of
laser-interferometric gravitational-wave detectors. Using a recently calculated
formula, accurate to second post-Newtonian (2PN) order [order , where
is the orbital velocity], for the frequency sweep () induced by
gravitational radiation damping, we study the statistical errors in the
determination of such source parameters as the ``chirp mass'' , reduced
mass , and spin parameters and (related to spin-orbit and
spin-spin effects, respectively). We find that previous results using template
phasing accurate to 1.5PN order actually underestimated the errors in ,
, and . For two inspiralling neutron stars, the measurement errors
increase by less than 16 percent.Comment: 14 pages, ReVTe
The Volume Inside a Black Hole
The horizon (the surface) of a black hole is a null surface, defined by those
hypothetical "outgoing" light rays that just hover under the influence of the
strong gravity at the surface. Because the light rays are orthogonal to the
spatial 2-dimensional surface at one instant of time, the surface of the black
hole is the same for all observers (i.e. the same for all coordinate
definitions of "instant of time"). This value is 4*(pi)* (2Gm/c^2)^2 for
nonspinning black holes, with G= Newton's constant, c= speed of light, and m=
mass of the black hole.
The 3-dimensional spatial volume inside a black hole, in contrast, depends
explicitly on the definition of time, and can even be time dependent, or zero.
We give examples of the volume found inside a standard, nonspinning spherical
black hole, for several different standard time-coordinate definitions.
Elucidating these results for the volume provides a new pedagogical resource of
facts already known in principle to the relativity community, but rarely worked
out.Comment: 17 pages, 5 figure
- …