On the r-mode spectrum of relativistic stars

We present a mathematically rigorous proof that the r-mode spectrum of relativistic stars to the rotational lowest order has a continuous part. A rigorous definition of this spectrum is given in terms of the spectrum of a continuous linear operator. This study verifies earlier results by Kojima (1998) about the nature of the r-mode spectrum.Comment: 6 pages, no figure

A new result on the Klein-Gordon equation in the background of a rotating black hole

This short paper should serve as basis for further analysis of a previously found new symmetry of the solutions of the wave equation in the gravitational field of a Kerr black hole. Its main new result is the proof of essential self-adjointness of the spatial part of a reduced normalized wave operator of the Kerr metric in a weighted L^2-space. As a consequence, it leads to a purely operator theoretic proof of the well-posedness of the initial value problem of the reduced Klein-Gordon equation in that field in that L^2-space and in this way generalizes a corresponding result of Kay (1985) in the case of the Schwarzschild black hole. It is believed that the employed methods are applicable to other separable wave equations

Quantifying excitations of quasinormal mode systems

Computations of the strong field generation of gravitational waves by black hole processes produce waveforms that are dominated by quasinormal (QN) ringing, a damped oscillation characteristic of the black hole. We describe here the mathematical problem of quantifying the QN content of the waveforms generated. This is done in several steps: (i) We develop the mathematics of QN systems that are complete (in a sense to be defined) and show that there is a quantity, the ``excitation coefficient,'' that appears to have the properties needed to quantify QN content. (ii) We show that incomplete systems can (at least sometimes) be converted to physically equivalent complete systems. Most notably, we give a rigorous proof of completeness for a specific modified model problem. (iii) We evaluate the excitation coefficient for the model problem, and demonstrate that the excitation coefficient is of limited utility. We finish by discussing the general question of quantification of QN excitations, and offer a few speculations about unavoidable differences between normal mode and QN systems.Comment: 27 pages, 14 figures. To be published in: J. Math. Phys. (1999

Financing North Dakota's Agriculture

Agricultural Finance,

Investigations of solutions of Einstein's field equations close to lambda-Taub-NUT

We present investigations of a class of solutions of Einstein's field equations close to the family of lambda-Taub-NUT spacetimes. The studies are done using a numerical code introduced by the author elsewhere. One of the main technical complication is due to the S3-topology of the Cauchy surfaces. Complementing these numerical results with heuristic arguments, we are able to yield some first insights into the strong cosmic censorship issue and the conjectures by Belinskii, Khalatnikov, and Lifschitz in this class of spacetimes. In particular, the current investigations suggest that strong cosmic censorship holds in this class. We further identify open issues in our current approach and point to future research projects.Comment: 24 pages, 12 figures, uses psfrag and hyperref; replaced with published version, only minor corrections of typos and reference

Doppler-tuned Bragg Spectroscopy of Excited Levels in He-Like Uranium: a discussion of the uncertainty contributions

We present the uncertainty discussion of a recent experiment performed at the GSI storage ring ESR for the accurate energy measurement of the He-like uranium 1s2p3P2- 1s2s3S1 intra-shell transition. For this propose we used a Johann-type Bragg spectrometer that enables to obtain a relative energy measurement between the He-like uranium transition, about 4.51 keV, and a calibration x-ray source. As reference, we used the Ka fluorescence lines of zinc and the Li-like uranium 1s22p2P3/2 - 1 s22s 2S1/2 intra-shell transition from fast ions stored in the ESR. A comparison of the two different references, i.e., stationary and moving x-ray source, and a discussion of the experimental uncertainties is presented

Doppler-tuned Bragg Spectroscopy of Excited Levels in He-Like Uranium: a discussion of the uncertainty contributions

We present the uncertainty discussion of a recent experiment performed at the GSI storage ring ESR for the accurate energy measurement of the He-like uranium 1s2p3P2- 1s2s3S1 intra-shell transition. For this propose we used a Johann-type Bragg spectrometer that enables to obtain a relative energy measurement between the He-like uranium transition, about 4.51 keV, and a calibration x-ray source. As reference, we used the Ka fluorescence lines of zinc and the Li-like uranium 1s22p2P3/2 - 1 s22s 2S1/2 intra-shell transition from fast ions stored in the ESR. A comparison of the two different references, i.e., stationary and moving x-ray source, and a discussion of the experimental uncertainties is presented

Feynman versus Bakamjian-Thomas in Light Front Dynamics

We compare the Bakamjian-Thomas (BT) formulation of relativistic few-body systems with light front field theories that maintain closer contact with Feynman diagrams. We find that Feynman diagrams distinguish Melosh rotations and other kinematical quantities belonging to various composite subsystem frames that correspond to different loop integrals. The BT formalism knows only the rest frame of the whole composite system, where everything is evaluated.Comment: 5 page

Doppler-tuned Bragg Spectroscopy of Excited Levels in He-Like Uranium: a discussion of the uncertainty contributions

We present the uncertainty discussion of a recent experiment performed at the GSI storage ring ESR for the accurate energy measurement of the He-like uranium 1s2p3P2- 1s2s3S1 intra-shell transition. For this propose we used a Johann-type Bragg spectrometer that enables to obtain a relative energy measurement between the He-like uranium transition, about 4.51 keV, and a calibration x-ray source. As reference, we used the Ka fluorescence lines of zinc and the Li-like uranium 1s22p2P3/2 - 1 s22s 2S1/2 intra-shell transition from fast ions stored in the ESR. A comparison of the two different references, i.e., stationary and moving x-ray source, and a discussion of the experimental uncertainties is presented