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Comment: 13 pages, 6 postscript figures
We consider the initial value problem for a massless scalar field in the Schwarzschild geometry. When constructed using a complex-frequency approach the necessary Green’s function splits into three components. We discuss all of these in some detail. (1) The contribution from the singularities (the quasinormal modes of the black hole) is approximated and the mode sum is demonstrated to converge after a certain well-defined time in the evolution. A dynamic description of the mode excitation is introduced and tested. (2) It is shown how a straightforward low-frequency approximation to the integral along the branch cut in the black-hole Green’s function leads to the anticipated power-law falloff at very late times. We also calculate higher order corrections to this tail and show that they provide an important complement to the leading orde...
Two simple model problems relevant for the gravitational-wave modes of relativistic stars are discussed. It is shown that the entire mode-spectrum can be obtained if one considers the modes as arising because of the trapping of gravitational waves by the spacetime curvature. The stellar fluid need play no dynamic role. Furthermore, it is shown that two distinct families of gravitational-wave modes exist. The first corresponds to waves trapped inside the star, while the second is similar to acoustic waves scattered off a hard sphere. An infinite number of the first kind of modes exist, but the latter family will only have a few members.
Contents 1. The Black Hole Equilibrium Problem; B. Carter.2. Stability of Black Holes; B.F. Whiting. 3. Separability of Wave Equations; E.G. Kalnins, et al. 4. Energy-Conservation Laws for Perturbed Stars and Black Holes; V.Ferrari. 5. Gravitational Collapse and Cosmic Censorship; R.M.Wald. 6. Disturbing the Black Hole; J.D. Bekenstein.7. Notes on Black Hole Fluctuations and Back-Reaction; B.L. Hu, et al. 8. Black Holes in Higher Curvature Gravity; R.C. Myers. 9. Micro-Structure of Black Holes and String Theory; S. Wadia. 10. Quantum Geometry and Black Holes; A. Ashtekar, K. Krasnov. 11. Black Holes, Global Monopole Charge and Quasi-Local Energy; N. Dadhich. 12. Kinematical Consequences of Inertial Forces in General Relativity; A.R. Prasanna, S. Iyer. 13. Gyroscopic Precession and Inertial Forces in General Relativity; R.Nayak. 14. An...
The first numerical study of axial (toroidal) pulsation modes of a slowly rotating relativistic star is presented. The calculation includes terms of first order in ε≡Ω(R3/M)1/2 « 1 (R is the radius, M is the mass, and Ω is the rotation frequency of the star) and accounts for effects due to the Coriolis force. Effects due to the centrifugal flattening of the star enter at order ε2 and are not included in the analysis. It is shown that increased rotation tends to decrease the damping times for prograde modes, while retrograde modes become longer lived. Specifically, we show that rotation affects the axial gravitational wave w-modes in this way. We also present the first relativistic calculation of the so-called r-modes (analogous to Rossby waves in the Earth's oceans). These have frequencies of the same order of magnitude as the rotation...
After an introductory overview of standard results for perturbed black holes (regarding quasinormal modes and power-law tails) we focus on three issues of recent interest. We discuss the possibility that the new generation of gravitational-wave detectors that are due to come online in the near future will be able to do “black-hole spectrocopy” by inferring black-hole parameters from quasinormal-mode signals. We summarise the recent effort to study perturbation of Kerr black holes using time-evolutions of the Teukolsky equation, and finally we present recent results that seem to indicate the existence of a new superradiance related phenomenon for rapidly spinning black holes.
This paper provides an overview of stellar instabilities as sources of gravitational waves. The aim is to put recent work on secular and dynamical instabilities in compact stars in context, and to summarize the current thinking about the detectability of gravitational waves from various scenarios. As a new generation of kilometre length interferometric detectors is now coming online this is a highly topical theme. The review is motivated by two key questions for future gravitational-wave astronomy: are the gravitational waves from various instabilities detectable? If so, what can these gravitational-wave signals teach us about neutron star physics? Even though we may not have clear answers to these questions, recent studies of the dynamical bar-mode instability and the secular r-mode instability have provided new insights into many of ...
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