Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

The Statistical Mechanics of Horizons and Black Hole Thermodynamics

Although we know that black holes are characterized by a temperature and an entropy, we do not yet have a satisfactory microscopic ``statistical mechanical'' explanation for black hole thermodynamics. I describe a new approach that attributes the thermodynamic properties to ``would-be gauge'' degrees of freedom that become dynamical on the horizon. For the (2+1)-dimensional black hole, this approach gives the correct entropy. (Talk given at the Pacific Conference on Gravitation and Cosmology, Seoul, February 1996.)Comment: 11 pages, LaTe

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review article originally published in 2002; available on-line at http://www.livingreviews.org

Searches for Gravitational Waves from Binary Neutron Stars: A Review

A new generation of observatories is looking for gravitational waves. These waves, emitted by highly relativistic systems, will open a new window for ob- servation of the cosmos when they are detected. Among the most promising sources of gravitational waves for these observatories are compact binaries in the final min- utes before coalescence. In this article, we review in brief interferometric searches for gravitational waves emitted by neutron star binaries, including the theory, instru- mentation and methods. No detections have been made to date. However, the best direct observational limits on coalescence rates have been set, and instrumentation and analysis methods continue to be refined toward the ultimate goal of defining the new field of gravitational wave astronomy.Comment: 30 pages, 5 Figures, to appear in "Short-Period Binary Stars: Observations, Analyses, and Results", Ed.s Eugene F. Milone, Denis A. Leahy, David W. Hobil

Gravitational Waves from Gravitational Collapse

Gravitational wave emission from the gravitational collapse of massive stars has been studied for more than three decades. Current state of the art numerical investigations of collapse include those that use progenitors with realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non--axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with advanced ground--based and future space--based interferometric observatories.Comment: 68 pages including 13 figures; revised version accepted for publication in Living Reviews in Relativity (http://www.livingreviews.org

Gravitational waves from single neutron stars: an advanced detector era survey

With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar "mountain" deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.Comment: 39 pages, 12 figures, 2 tables. Chapter of the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action 1304. Minor corrections to match published versio

Physics, Astrophysics and Cosmology with Gravitational Waves

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.Comment: 137 pages, 16 figures, Published version <http://www.livingreviews.org/lrr-2009-2

Spin and quadrupole contributions to the motion of astrophysical binaries

Compact objects in general relativity approximately move along geodesics of spacetime. It is shown that the corrections to geodesic motion due to spin (dipole), quadrupole, and higher multipoles can be modeled by an extension of the point mass action. The quadrupole contributions are discussed in detail for astrophysical objects like neutron stars or black holes. Implications for binaries are analyzed for a small mass ratio situation. There quadrupole effects can encode information about the internal structure of the compact object, e.g., in principle they allow a distinction between black holes and neutron stars, and also different equations of state for the latter. Furthermore, a connection between the relativistic oscillation modes of the object and a dynamical quadrupole evolution is established.Comment: 43 pages. Proceedings of the 524. WE-Heraeus-Seminar "Equations of Motion in Relativistic Gravity". v2: fixed reference. v3: corrected typos in eqs. (1), (57), (85

Composition change-driven texturing and doping in solution-processed SnSe thermoelectric thin films

The discovery of SnSe single crystals with record high thermoelectric efficiency along the b-axis has led to the search for ways to synthesize polycrystalline SnSe with similar efficiencies. However, due to weak texturing and difficulties in doping, such high thermoelectric efficiencies have not been realized in polycrystals or thin films. Here, we show that highly textured and hole doped SnSe thin films with thermoelectric power factors at the single crystal level can be prepared by solution process. Purification step in the synthetic process produced a SnSe-based chalcogenidometallate precursor, which decomposes to form the SnSe2 phase. We show that the strong textures of the thin films in the b???c plane originate from the transition of two dimensional SnSe2 to SnSe. This composition change-driven transition offers wide control over composition and doping of the thin films. Our optimum SnSe thin films exhibit a thermoelectric power factor of 4.27 ??W cm???1 K???2

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.Comment: 101 pages, 18 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.org