6738139
Wave propagation in gravitational systems: Completeness of quasinormal modes.
The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM’s) of the Klein-Gordon (KG) equation with different effective potentials V (x). In this paper we present a systematic study of the relation between the structure of the QNM’s of the KG equation and the form of V (x). In particular, we determine the requirements on V (x) in order for the QNM’s to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM’s do not form a complete set. For such systems, we show that a complete set of QNM’s can often be obtained by introducing an infinitesimal change in the effective potential.
42491588
Probing the interior of neutron stars with gravitational waves.
We show here how the internal structure of a neutron star can be inferred from its gravitational wave spectrum. Under the premise that the frequencies and damping rates of a few w-mode oscillations are found, we apply an inversion scheme to determine its mass, radius, and density distribution. In addition, an accurate equation of state of nuclear matter can also be determined.
119695730
SUSY Transformations for Quasinormal and Total-Transmission Modes of Open Systems
Quasinormal modes are the counterparts in open systems of normal modes in conservative systems; defined by outgoing-wave boundary conditions, they have complex eigenvalues. The conditions are studied for a system to have a supersymmetric(SUSY) partner with the same complex quasinormal-mode spectrum (or the same except for one eigenvalue). The discussion naturally includes total-transmission modes as well(incoming at one extreme and outgoing at the other). Several types of SUSY transformations emerge, and each is illustrated with examples, including the transformation among different Poschl-Teller potentials and the well-known identity in spectrum between the two parity sectors of linearized gravitational waves propagating on a Schwarzschild background. In contrast to the case of normal modes, there may be multiple essentially isospectral partners, each missing a different state. The SUSY transformation preserves orthonormality under a bilinear map which is the analog of the usual inner product for conservative systems. SUSY transformations can lead to doubled quasinormal and total-transmission modes; this phenomenon is analysed and illustrated. The existence or otherwise of SUSY partners is also relevant to the question of inversion: are open wave systems uniquely determined by their complex spectra?
119332377
QUASINORMAL MODES OF DIRTY BLACK HOLES
Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.
120306757
Quasinormal-mode expansion for waves in open systems
An open system is not conservative because energy can escape to the outside. As a result, the time-evolution operator is not Hermitian in the usual sense and the eigenfunctions (factorized solutions in space and time) are no longer normal modes but quasinormal modes (QNMs) whose frequencies $\ensuremath{\omega}$ are complex. Qausinormal-mode analysis has been a powerful tool for investigating open systems. Previous studies have been mostly system specific, and use a few QNMs to provide approximate descriptions. Here the authors review developments that lead to a unifying treatment. The formulation leads to a mathematical structure in close analogy to that in conservative, Hermitian systems. Hence many of the mathematical tools for the latter can be transcribed. Emphasis is placed on those cases in which the QNMs form a complete set and thus give an exact description of the dynamics. In situations where the QNMs are not complete, the ``remainder'' is characterized. Applications to optics in microspheres and to gravitational waves from black holes are given as examples. The second-quantized theory is sketched. Directions for further development are outlined.
119211222
Separation of space–time and matter in polar oscillations of compact stars
In polar oscillations of compact stars dynamical changes in spacetime and matter are in general coupled together. Based on the theory of stellar pulsation proposed by Allen et al. [Phys. Rev. D 58, 124012 (1998)], we establish a feasible approximation scheme to separate spacetime from matter in such oscillations. Two independent second-order ordinary differential equations are obtained, which lead to accurate determination of p-mode and w-mode quasi-normal modes of compact stars, respectively.
18208373
Neutrino mixing due to a violation of the equivalence principle.
Massless neutrinos will mix if their couplings to gravity are flavor dependent, i.e., violate the principle of equivalence. Because the gravitational interaction grows with neutrino energy, the solar neutrino problem and the recent atmospheric neutrino data may be simultaneously explained by violations at the level of 10[sup [minus]14] to 10[sup [minus]17] or smaller. This possibility is severely constrained by present accelerator neutrino experiments and will be preeminently tested in proposed long-base-line accelerator neutrino experiments.
7271721
Properties of the dilaton.
Gauge models which possess a hierarchy of mass scales may exhibit a pseudo-Goldstone boson, the dilaton, of the scale symmetry. Properties of the dilaton are studied in a technicolor model, where the technifermion chiral condensation scale differs from the confinement scale. The dilaton exhibits properties very similar to the elementary Higgs boson of the standard model. It is distinguished from the Higgs boson by its Goldstone nature, which is manifested in an enhanced multidilaton production. Estimates for the dilaton mass and lifetime are given and various production mechanisms are discussed. Prospects for detecting the dilaton in its associated production with W or Z and in W and Z decays are stressed.
8754080
Schwinger-Dyson equation approach to chiral symmetry breaking in an external magnetic field.
We develop a method for using the nonperturbative Schwinger-Dyson equation to study chiral symmetry breaking in an external field. We apply it to massless QED in a constant magnetic field and obtain a nontrivial solution for the fermion self-energy at weak coupling, suggesting that chiral symmetry is dynamically broken. {copyright} {ital 1996 The American Physical Society.}