4,697 research outputs found
The response of interferometric gravitational wave detectors
The derivation of the response function of an interferometric gravitational
wave detector is a paradigmatic calculation in the field of gravitational wave
detection. Surprisingly, the standard derivation of the response wave detectors
makes several unjustifiable assumptions, both conceptual and quantitative,
regarding the coordinate trajectory and coordinate velocity of the null
geodesic the light travels along. These errors, which appear to have remained
unrecognized for at least 35 years, render the "standard" derivation inadequate
and misleading as an archetype calculation. Here we identify the flaws in the
existing derivation and provide, in full detail, a correct derivation of the
response of a single-bounce Michelson interferometer to gravitational waves,
following a procedure that will always yield correct results; compare it to the
"standard", but incorrect, derivation; show where the earlier mistakes were
made; and identify the general conditions under which the "standard" derivation
will yield correct results. By a fortuitous set of circumstances, not generally
so, the final result is the same in the case of Minkowski background spacetime,
synchronous coordinates, transverse-traceless gauge metric perturbations, and
arm mirrors at coordinate rest.Comment: 10 pages, one figure, as accepted to PR
Lagrangian perfect fluids and black hole mechanics
The first law of black hole mechanics (in the form derived by Wald), is
expressed in terms of integrals over surfaces, at the horizon and spatial
infinity, of a stationary, axisymmetric black hole, in a diffeomorphism
invariant Lagrangian theory of gravity. The original statement of the first law
given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system
contained, in addition, volume integrals of the fluid fields, over a spacelike
slice stretching between these two surfaces. When applied to the
Einstein-perfect fluid system, however, Wald's methods yield restricted
results. The reason is that the fluid fields in the Lagrangian of a gravitating
perfect fluid are typically nonstationary. We therefore first derive a first
law-like relation for an arbitrary Lagrangian metric theory of gravity coupled
to arbitrary Lagrangian matter fields, requiring only that the metric field be
stationary. This relation includes a volume integral of matter fields over a
spacelike slice between the black hole horizon and spatial infinity, and
reduces to the first law originally derived by Bardeen, Carter and Hawking when
the theory is general relativity coupled to a perfect fluid. We also consider a
specific Lagrangian formulation for an isentropic perfect fluid given by
Carter, and directly apply Wald's analysis. The resulting first law contains
only surface integrals at the black hole horizon and spatial infinity, but this
relation is much more restrictive in its allowed fluid configurations and
perturbations than that given by Bardeen, Carter and Hawking. In the Appendix,
we use the symplectic structure of the Einstein-perfect fluid system to derive
a conserved current for perturbations of this system: this current reduces to
one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2
Removing non-stationary, non-harmonic external interference from gravitational wave interferometer data
We describe a procedure to identify and remove a class of non-stationary and
non-harmonic interference lines from gravitational wave interferometer data.
These lines appear to be associated with the external electricity main
supply, but their amplitudes are non-stationary and they do not appear at
harmonics of the fundamental supply frequency. We find an empirical model able
to represent coherently all the non-harmonic lines we have found in the power
spectrum, in terms of an assumed reference signal of the primary supply input
signal. If this signal is not available then it can be reconstructed from the
same data by making use of the coherent line removal algorithm that we have
described elsewhere. All these lines are broadened by frequency changes of the
supply signal, and they corrupt significant frequency ranges of the power
spectrum. The physical process that generates this interference is so far
unknown, but it is highly non-linear and non-stationary. Using our model, we
cancel the interference in the time domain by an adaptive procedure that should
work regardless of the source of the primary interference. We have applied the
method to laser interferometer data from the Glasgow prototype detector, where
all the features we describe in this paper were observed. The algorithm has
been tuned in such a way that the entire series of wide lines corresponding to
the electrical interference are removed, leaving the spectrum clean enough to
detect signals previously masked by them. Single-line signals buried in the
interference can be recovered with at least 75 % of their original signal
amplitude.Comment: 14 pages, 5 figures, Revtex, psfi
Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame
The Planck spectrum of thermal scalar radiation is derived suggestively
within classical physics by the use of an accelerating coordinate frame. The
derivation has an analogue in Boltzmann's derivation of the Maxwell velocity
distribution for thermal particle velocities by considering the thermal
equilibrium of noninteracting particles in a uniform gravitational field. For
the case of radiation, the gravitational field is provided by the acceleration
of a Rindler frame through Minkowski spacetime. Classical zero-point radiation
and relativistic physics enter in an essential way in the derivation which is
based upon the behavior of free radiation fields and the assumption that the
field correlation functions contain but a single correlation time in thermal
equilibrium. The work has connections with the thermal effects of acceleration
found in relativistic quantum field theory.Comment: 23 page
Evolving a puncture black hole with fixed mesh refinement
We present an algorithm for treating mesh refinement interfaces in numerical
relativity. We detail the behavior of the solution near such interfaces located
in the strong field regions of dynamical black hole spacetimes, with particular
attention to the convergence properties of the simulations. In our applications
of this technique to the evolution of puncture initial data with vanishing
shift, we demonstrate that it is possible to simultaneously maintain second
order convergence near the puncture and extend the outer boundary beyond 100M,
thereby approaching the asymptotically flat region in which boundary condition
problems are less difficult and wave extraction is meaningful.Comment: 18 pages, 12 figures. Minor changes, final PRD versio
Gravitational wave astronomy
The first decade of the new millenium should see the first direct detections
of gravitational waves. This will be a milestone for fundamental physics and it
will open the new observational science of gravitational wave astronomy. But
gravitational waves already play an important role in the modeling of
astrophysical systems. I review here the present state of gravitational
radiation theory in relativity and astrophysics, and I then look at the
development of detector sensitivity over the next decade, both on the ground
(such as LIGO) and in space (LISA). I review the sources of gravitational waves
that are likely to play an important role in observations by first- and
second-generation interferometers, including the astrophysical information that
will come from these observations. The review covers some 10 decades of
gravitational wave frequency, from the high-frequency normal modes of neutron
stars down to the lowest frequencies observable from space. The discussion of
sources includes recent developments regarding binary black holes, spinning
neutron stars, and the stochastic background.Comment: 29 pages, 2 figures, as submitted for special millenium issue of
Classical and Quantum Gravit
Quasi-Asimptotically Flat Spacetimes and Their ADM Mass
We define spacetimes that are asymptotically flat, except for a deficit solid
angle , and present a definition of their ``ADM'' mass, which is finite
for this class of spacetimes, and, in particular, coincides with the value of
the parameter of the global monopole spacetime studied by Vilenkin and
Barriola . Moreover, we show that the definition is coordinate independent, and
explain why it can, in some cases, be negative.Comment: Late
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
A stable static Universe?
Starting from the assumption that general relativity might be an emergent
phenomenon showing up at low-energies from an underlying microscopic structure,
we re-analyze the stability of a static closed Universe filled with radiation.
In this scenario, it is sensible to consider the effective general-relativistic
configuration as in a thermal contact with an "environment" (the role of
environment can be played, for example, by the higher-dimensional bulk or by
the trans-Planckian degrees of freedom). We calculate the free energy at a
fixed temperature of this radiation-filled static configuration. Then, by
looking at the free energy we show that the static Einstein configuration is
stable under the stated condition.Comment: 6 pages, no figures; uses revtex4; version accepted for publication;
some phrasing changed; wrong coefficient correcte
On the Solution to the "Frozen Star" Paradox, Nature of Astrophysical Black Holes, non-Existence of Gravitational Singularity in the Physical Universe and Applicability of the Birkhoff's Theorem
Oppenheimer and Snyder found in 1939 that gravitational collapse in vacuum
produces a "frozen star", i.e., the collapsing matter only asymptotically
approaches the gravitational radius (event horizon) of the mass, but never
crosses it within a finite time for an external observer. Based upon our recent
publication on the problem of gravitational collapse in the physical universe
for an external observer, the following results are reported here: (1) Matter
can indeed fall across the event horizon within a finite time and thus BHs,
rather than "frozen stars", are formed in gravitational collapse in the
physical universe. (2) Matter fallen into an astrophysical black hole can never
arrive at the exact center; the exact interior distribution of matter depends
upon the history of the collapse process. Therefore gravitational singularity
does not exist in the physical universe. (3) The metric at any radius is
determined by the global distribution of matter, i.e., not only by the matter
inside the given radius, even in a spherically symmetric and pressureless
gravitational system. This is qualitatively different from the Newtonian
gravity and the common (mis)understanding of the Birkhoff's Theorem. This
result does not contract the "Lemaitre-Tolman-Bondi" solution for an external
observer.Comment: 8 pages, 4 figures, invited plenary talk at "The first Galileo-Xu
Guangqi conference", Shanghai, China, 2009. To appear in International
Journal of Modern Physics D (2010
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