Abstract: The aim of this thesis is to investigate the effects that a lightlike singular hypersurface can have on a congruence of timelike (spacelike) geodesics and to extend the existing theory to the case of null geodesics.
The introduction discusses the applications of singular hypersurfaces for the description of physical phenomena, their major classfications and includes a short discussion of the two theoretical approaches that exist to study singular hypersurfaces. The second chapter contains detailed description of these approaches. The theoretical frameworks for both cases of lightlike and timelike (spacelike) hypersurfaces are developed. This chapter also discusses the application of these theories to the case when the hypersurface contains a plane fronted lightlike signal.
The final chapter starts with a discussion of the effects that a lightlike singular hypersurface can have on a congruence of timelike (spacelike) geodesics. A new approach to these calculations is presented together with an extension of the theory to the case of a congruence of null geodesics. At
the end of the chapter a concrete example and its similarities with the case of timelike geodesics is discussed.
In conclusion, the thesis suggests a new mathematical framework for describing a congruence of null geodesics crossing a singular null hypersurface. The results may be applied in experimental physics to detect impulsive signals which are located in singular null hypersurfaces and to this end there
is a discussion of the properties and possibilities for a detector of impulsive lightlike signals, which include gravitational waves.Found in: osebiKeywords: singular hypersurface, impulsive signal, gravitational wave, null geodesic, timelike (spacelike) geodesicPublished: 16.05.2016; Views: 5656; Downloads: 223 Fulltext (475,54 KB)