425779
Quasinormal mode expansion for linearized waves in gravitational systems.
The quasinormal modes (QNM's) of gravitational systems modeled by the Klein-Gordon equation with effective potentials are studied in analogy to the QNM's of optical cavities. Conditions are given for the QNM's to form a complete set, i.e., for the Green's function to be expressible as a sum over QNM's, answering a conjecture by Price and Husain [Phys. Rev. Lett. {\bf 68}, 1973 (1992)]. In the cases where the QNM sum is divergent, procedures for regularization are given. The crucial condition for completeness is the existence of spatial discontinuities in the system, e.g., the discontinuity at the stellar surface in the model of Price and Husain.
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.
17520758
Perturbative Approach to the Quasinormal Modes of Dirty Black Holes
Using a recently developed perturbation theory for quasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasistatic perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.
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.
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.
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?
16320121
Possible violation of the equivalence principle by neutrinos.
We consider the effect of a long-range, flavor-changing tensor interaction of possible gravitational origin. Neutrino-mixing experiments provide the most sensitive probe to date for such forces{emdash}testing the equivalence principle at levels below 10{sup {minus}20}. Here we justify and generalize a formalism for describing such effects. The constraints from neutrino-mixing experiments on gravitationally induced mixing are calculated. Our detailed analysis of the atmospheric neutrino data confirms a remarkable result: the atmospheric neutrino data imply the same size violation of the equivalence principle as do the solar neutrino data. Additional tests of this suggestive result are discussed. {copyright} {ital 1996 The American Physical Society.}
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.
17801115
Solar neutrinos and the principle of equivalence.
We study the proposed solution of the solar neutrino problem which requires a flavor nondiagonal coupling of neutrinos to gravity. We adopt a phenomenological point of view and investigate the consequences of the hypothesis that the neutrino weak interaction eigenstates are linear combinations of the gravitational eigenstates which have slightly different couplings to gravity, ${\mathit{f}}_{1}$G and ${\mathit{f}}_{2}$G, \ensuremath{\Vert}${\mathit{f}}_{1}$-${\mathit{f}}_{2}$\ensuremath{\Vert}\ensuremath{\ll}1, corresponding to a difference in redshift between electron and muon neutrinos, \ensuremath{\Delta}z/(1+z)\ensuremath{\sim}\ensuremath{\Vert}${\mathit{f}}_{1}$-${\mathit{f}}_{2}$\ensuremath{\Vert}. Our ${\mathrm{\ensuremath{\chi}}}^{2}$ analysis of the available solar neutrino data on observed event rates rules out most of the relevant parameter space, allowing only \ensuremath{\Vert}${\mathit{f}}_{1}$-${\mathit{f}}_{2}$\ensuremath{\Vert}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}14}$ for small values of the mixing angle [2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$\ensuremath{\lesssim}${\mathrm{sin}}^{2}$(2${\mathrm{\ensuremath{\theta}}}_{\mathit{G}}$)\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}2}$] and ${10}^{\mathrm{\ensuremath{-}}16}$\ensuremath{\lesssim}\ensuremath{\Vert}${\mathit{f}}_{1}$-${\mathit{f}}_{2}$\ensuremath{\Vert}\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}15}$ for large mixing [0.6\ensuremath{\lesssim}${\mathrm{sin}}^{2}$(2${\mathrm{\ensuremath{\theta}}}_{\mathit{G}}$)\ensuremath{\lesssim}0.9]. We show that the recoil-electron spectrum measured by the Kamiokande II Collaboration can be used to exclude part of the allowed regions obtained above. We analyze the prospects of using future spectral measurements of solar neutrinos to distinguish the oscillation mechanism due to the violation of the equivalence principle from more conventional mechanisms which require neutrinos to have nondegenerate masses. We find that, for small mixing angles, the flavor nondiagonal coupling to gravity leads to predictions regarding the shape of the $^{8}\mathrm{neutrino}$ spectrum which will be distinguishable in the upcoming SNO and Super-Kamiokande experiments and which are independent of solar models.
31381865
Can the Sun shed light on neutrino gravitational interactions?
We have examined the effects of a large gravitational field on the phenomenon of neutrino oscillations as contemplated in the Mikheyev-Smirnov-Wolfenstein mechanism. We find that the Sun's gravitational field would amplify any small breakdown in the universality of the gravitational coupling by many orders of magnitude. A breakdown of only 1 part in 10{sup 14} would still make the gravitational effect comparable to the conventional weak interaction. The differing energy dependences of the two level-crossing mechanisms can therefore be used as a very sensitive tool to test the conventional universality hypothesis.