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Classical and Quantum Aspects of Gravitation and Cosmology
These are the proceedings of the XVIII Conference of the Indian Association
for General Relativity and Gravitation (IAGRG) held at the Institute of
Mathematical Sciences, Madras, INDIA during Feb. 15-17, 1996. The Conference
was dedicated the late Prof. S. Chandrasekhar.
The proceedings consists of 17 articles on:
- Chandrasekhar's work (N. Panchapkesan);
- Vaidya-Raychaudhuri Lecture (C.V. Vishveshwara)
- Gravitational waves (B.R. Iyer, R. Balasubramanian)
- Gravitational Collapse (T.P. Singh)
- Accretion on black hole (S. Chakrabarti)
- Cosmology (D. Munshi, S. Bharadwaj, G.S. Mohanty, P. Bhattacharjee);
- Classical GR (S. Kar, D.C. Srivatsava)
- Quantum aspects (J. Maharana, Saurya Das, P. Mitra, G. Date, N.D. Hari
Dass)
The body of THIS article contains ONLY the title, contents, foreword,
organizing committees, preface, list of contributed talks and list of
participants. The plenery talks are available at:
http://www.imsc.ernet.in/physweb/Conf/ both as post-script files of individual
articles and also as .uu source files. For further information please send
e-mail to [email protected]: 12 pages, latex, needs psfig.tex macros. Latex the file run.tex.
These Proceedings of the XVIII IAGRG Conference are available at
http://www.imsc.ernet.in/physweb/Conf/ MINOR TYPO's in the ABSTRACT correcte
Workshop on gravitational waves
In this article we summarise the proceedings of the Workshop on Gravitational
Waves held during ICGC-95. In the first part we present the discussions on 3PN
calculations (L. Blanchet, P. Jaranowski), black hole perturbation theory (M.
Sasaki, J. Pullin), numerical relativity (E. Seidel), data analysis (B.S.
Sathyaprakash), detection of gravitational waves from pulsars (S. Dhurandhar),
and the limit on rotation of relativistic stars (J. Friedman). In the second
part we briefly discuss the contributed papers which were mainly on detectors
and detection techniques of gravitational waves.Comment: 18 pages, kluwer.sty, no figure
Improved filters for gravitational waves from inspiraling compact binaries
The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) the introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of the Padé approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (smaller biases) than the standard Taylor approximants, but also converge faster and monotonically. The presently available (v/c)^5-accurate post-Newtonian results can be used to construct P-approximate wave forms that provide overlaps with the exact wave form larger than 96.5%, implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 10–15 % that would be detectable using standard post-Newtonian approximants
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
Probing the non-linear structure of general relativity with black hole binaries
Observations of the inspiral of massive binary black holes (BBH) in the Laser
Interferometer Space Antenna (LISA) and stellar mass binary black holes in the
European Gravitational-Wave Observatory (EGO) offer an unique opportunity to
test the non-linear structure of general relativity. For a binary composed of
two non-spinning black holes, the non-linear general relativistic effects
depend only on the masses of the constituents. In a recent letter, we explored
the possibility of a test to determine all the post-Newtonian coefficients in
the gravitational wave-phasing.
However, mutual covariances dilute the effectiveness of such a test. In this
paper, we propose a more powerful test in which the various post-Newtonian
coefficients in the gravitational wave phasing are systematically measured by
treating three of them as independent parameters and demanding their mutual
consistency. LISA (EGO) will observe BBH inspirals with a signal-to-noise ratio
of more than 1000 (100) and thereby test the self-consistency of each of the
nine post-Newtonian coefficients that have so-far been computed, by measuring
the lower order coefficients to a relative accuracy of
(respectively, ) and the higher order coefficients to a relative
accuracy in the range -0.1 (respectively, -1).Comment: 5 pages, 4 figures. Revised version, accepted for publication in
Phys. Rev
Centrifugal Force and Ellipticity behaviour of a slowly rotating ultra compact object
Using the optical reference geometry approach, we have derived in the
following, a general expression for the ellipticity of a slowly rotating fluid
configuration using Newtonian force balance equation in the conformally
projected absolute 3-space, in the realm of general relativity. Further with
the help of Hartle-Thorne (H-T) metric for a slowly rotating compact object, we
have evaluated the centrifugal force acting on a fluid element and also
evaluated the ellipticity and found that the centrifugal reversal occurs at
around , and the ellipticity maximum at around . The result has been compared with that of Chandrasekhar and
Miller which was obtained in the full 4-spacetime formalism
Higher signal harmonics, LISA's angular resolution, and dark energy
It is generally believed that the angular resolution of the Laser
Interferometer Space Antenna (LISA) for binary supermassive black holes (SMBH)
will not be good enough to identify the host galaxy or galaxy cluster. This
conclusion, based on using only the dominant harmonic of the binary SMBH
signal, changes substantially when higher signal harmonics are included in
assessing the parameter estimation problem. We show that in a subset of the
source parameter space the angular resolution increases by more than a factor
of 10, thereby making it possible for LISA to identify the host galaxy/galaxy
cluster. Thus, LISA's observation of certain binary SMBH coalescence events
could constrain the dark energy equation of state to within a few percent,
comparable to the level expected from other dark energy missions.Comment: 15 pages, no figures. Final version to appear in Phys. Rev.
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
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