On the stability of the massive scalar field in Kerr space-time

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon equation, describing the propagation of a scalar field in the background of a rotating (Kerr-) black hole. Results suggest that the stability of the field depends crucially on its mass $\mu$. Among others, the paper provides an improved bound for $\mu$ above which the solutions of the reduced, by separation in the azimuth angle in Boyer-Lindquist coordinates, Klein-Gordon equation are stable. Finally, it gives new formulations of the reduced equation, in particular, in form of a time-dependent wave equation that is governed by a family of unitarily equivalent positive self-adjoint operators. The latter formulation might turn out useful for further investigation. On the other hand, it is proved that from the abstract properties of this family alone it cannot be concluded that the corresponding solutions are stable

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

Correlations in hot and dense quark matter

We present a relativistic three-body equation to investigate three-quark clusters in hot and dense quark matter. To derive such an equation we use the Dyson equation approach. The equation systematically includes the Pauli blocking factors as well as the self energy corrections of quarks. Special relativity is realized through the light front form. Presently we use a zero-range force and investigate the Mott transition.Comment: 6 pages, 4 figure, Few-Body Systems style file

n Voorlopige model vir die sistematiese beskrywing van gebruikersvriendelikheid in woordeboeke

Die gebruikersperspektief staan tans sentraal in die leksikografiese gesprek. Dit spruit uit die beginsel dat enige woordeboek in die eerste plek vir gebruik deur 'n bepaalde teikengebruikersgroep bedoel moet wees, en as sodanig moet die woordeboek op daardie gebrui-kersgroep afgestem wees — dit moet gebruikersvriendelik wees. In hierdie artikel word van die standpunt uitgegaan dat die gebruik van 'n woordeboek as 'n kommunikatiewe handeling begryp moet word, wat die geleentheid bied om insigte uit die kommunikasiewetenskap in die metalek-sikografie te benut. Na aanleiding van die algemene kommunikasiemodel vir interpersoonlike kommunikasie wat in die literatuur oor kommunikasiewetenskap voorkom, word 'n leksikogra-fiese kommunikasiemodel voorgestel. Uit hierdie model kan minstens elf leksikografiese para-meters afgelei word aan die hand waarvan gebruikersvriendelikheid in woordeboeke sistematies beskryf kan word. Die struktuur wat hierdie parameters aan 'n gesprek oor gebruikersvriendelik-heid in woordeboeke kan gee, bemiddel die formulering van die ware doel van 'n gebruikers-vriendelike woordeboek. Sleutelwoorde: gebruik, gebruiker, gebruikersperspektief, gebruikersver-wysingsraamwerk, gebruikersvriendelikheid, kanaal, kommunikasiemodel, konteks, leksikograaf, leksikografiese kommunikasiemodel, medium, meta-teks, stylgids, terugvoer, werklike doel, woordeboek, woordeboekpla