Quasi-normal modes of stars and Black holes
TL;DR: 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.
Abstract: 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-Nordstrom, 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.
Citations
More filters
TL;DR: Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging.
Abstract: The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.
3,394 citations
Cites background from "Quasi-normal modes of stars and Bla..."
...Another is black-hole perturbation theory (see [261, 201, 323, 37] for reviews)....
[...]
...All results of black hole perturbation agree precisely with them1 → 0 limit of the PN results, up to the highest PN order where they can be compared (for reviews of earlier work see [261, 201, 323])....
[...]
TL;DR: Quasinormal modes are eigenmodes of dissipative systems as discussed by the authors, and they serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, such as viscosity, conductivity and diffusion constants.
Abstract: Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.
1,592 citations
TL;DR: In this paper, a prescription for computing Minkowski-space correlators from AdS/CFT correspondence was formulated and shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in two dimensions.
Abstract: We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence. This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole. Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature = 4 supersymmetric Yang-Mills theory in the strong coupling limit. We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.
1,478 citations
Cites background from "Quasi-normal modes of stars and Bla..."
...(2)For reviews and references on quasinormal modes in asymptotically flat spacetimes see [16, 17]....
[...]
TL;DR: In this paper, a review of recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, anti-de Sitter/conformal field theory interpretation, and holographic superconductors.
Abstract: Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past 10 years in string theory, brane-world models, and quantum gravity. Through the famous gauge/gravity duality, proper oscillations of perturbed black holes, called quasinormal modes, allow for the description of the hydrodynamic regime in the dual finite temperature field theory at strong coupling, which can be used to predict the behavior of quark-gluon plasmas in the nonperturbative regime. On the other hand, the brane-world scenarios assume the existence of extra dimensions in nature, so that multidimensional black holes can be formed in a laboratory experiment. All this stimulated active research in the field of perturbations of higher-dimensional black holes and branes during recent years. In this review recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, anti--de Sitter/conformal field theory interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.
1,070 citations
University of Mississippi1, University of Lisbon2, Institut d'Astrophysique de Paris3, Perimeter Institute for Theoretical Physics4, Sapienza University of Rome5, California Institute of Technology6, University of Cambridge7, Cornell University8, Max Planck Society9, Montana State University10, Princeton University11, University of Oxford12, McMaster University13, University of Aveiro14, University of Tübingen15, Naresuan University16, Rochester Institute of Technology17, University of Oldenburg18, Georgia Institute of Technology19, University of Illinois at Urbana–Champaign20, University of Florida21, University of Wisconsin–Milwaukee22, The Chinese University of Hong Kong23, Northwestern University24, Case Western Reserve University25, Sao Paulo State University26, Cardiff University27, Imperial College London28, Grand Valley State University29, Kyoto University30
TL;DR: In this article, a catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory is presented, and the current understanding of the structure and dynamics of compact objects in these theories is summarized.
Abstract: One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.
1,066 citations
References
More filters
Book•
01 Jan 1978
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Abstract: This book gives a self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations. Parts and chapter titles are as follows: fundamentals - ordinary differential equations, difference equations; local analysis - approximate solution of linear differential equations, approximate solution of nonlinear differential equations, approximate solution of difference equations, asymptotic expansion of integrals; perturbation methods - perturbation series, summation series; and global analysis - boundary layer theory, WKB theory, multiple-scale analysis. An appendix of useful formulas is included. 147 figures, 43 tables. (RWR)
4,776 citations
"Quasi-normal modes of stars and Bla..." refers background in this paper
...A more general form can be found [82, 41] which is valid for complex potentials....
[...]
27 Jul 1983
TL;DR: In this paper, the soft file of a book collection of black holes white dwarfs and neutron stars can be downloaded and the book can be found on-line in this site.
Abstract: Only for you today! Discover your favourite black holes white dwarfs and neutron stars book right here by downloading and getting the soft file of the book. This is not your time to traditionally go to the book stores to buy a book. Here, varieties of book collections are available to download. One of them is this black holes white dwarfs and neutron stars as your preferred book. Getting this book b on-line in this site can be realized now by visiting the link page to download. It will be easy. Why should be here?
4,305 citations
Book•
01 Jan 1983TL;DR: In a course of lectures on the underlying mathematical structures of classical gravitation theory given in 1978, Brandon Carter as discussed by the authors began with the statement ‘If I had been asked five years ago to prepare a course for recent developments in classical gravity theory, I would not have hesitated on the classical theory of black holes as a central topic of discussion. But I am grateful to them for their courtesy in assigning to me this privilege.
Abstract: In a course of lectures on the ‘underlying mathematical structures of classical gravitation theory’ given in 1978, Brandon Carter began with the statement ‘If I had been asked five years ago to prepare a course of lectures on recent developments in classical gravitation theory, I would not have hesitated on the classical theory of black holes as a central topic of discussion. However, the most important developments in gravitational theory during the last three or four years have not been in the classical domain at all…’ Carter is undoubtedly right in his assessment that the mathematical theory of black holes has not been in the mainstream of research in relativity since 1973. I therefore find it difficult to understand why the organizers of this meeting should have chosen precisely this topic for the opening talk of this meeting. But I am grateful to them for their courtesy in assigning to me this privilege.
4,165 citations
TL;DR: In this article, it is argued that a convective dynamo can also generate a very strong dipole field after the merger of a neutron star binary, but only if the merged star survives for as long as about 10-100 ms.
Abstract: It is proposed that the main observational signature of magnetars, high-field neutron stars, is gamma-ray bursts powered by their vast reservoirs of magnetic energy. If they acquire large recoils, most magnetars are unbound from the Galaxy or reside in an extended, weakly bound Galactic corona. There is evidence that the soft gamma repeaters are young magnetars. It is argued that a convective dynamo can also generate a very strong dipole field after the merger of a neutron star binary, but only if the merged star survives for as long as about 10-100 ms. Several mechanisms which could impart a large recoil to these stars at birth, sufficient to escape from the Galactic disk, are discussed.
2,482 citations
"Quasi-normal modes of stars and Bla..." refers background in this paper
...This is an interesting possibility considering the recent discovery of so-called magnetars: Neutron stars with extreme magnetic fields [81]....
[...]
TL;DR: In this article, it was shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and therefore remain stable if subjected to a small nonspherical perturbation.
Abstract: It is shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and will therefore remain stable if subjected to a small nonspherical perturbation.
2,105 citations
Additional excerpts
...Contents...
[...]