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Title:Properties of Null Hypersurfaces
Authors:Demirtshyan, Hovhannes (Author)
O'Loughlin, Martin (Mentor) More about this mentor... New window
Files:.pdf Hovhannes_Demirtshyan.pdf (475,54 KB)
 
Language:English
Work type:Master's thesis/paper (mb22)
Tipology:2.09 - Master's Thesis
Organization:FN - School of Science
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.
Keywords:singular hypersurface, impulsive signal, gravitational wave, null geodesic, timelike (spacelike) geodesic
Year of publishing:2016
Source:Nova Gorica
COBISS_ID:4318203 Link is opened in a new window
URN:URN:SI:UNG:REP:4I1GBLCJ
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Secondary language

Language:Slovenian
Abstract:Cilj te magistrske naloge je raziskovanje učinkov, ki jih lahko ima singularna svetlobna hiperploskev na ujemanje časovnih (prostorskih) geodetskih črt. Pri tem želimo razširiti obstoječo teorijo za primer ničelnih geodetskih črt. V uvodu obravnavamo uporabo singularnih hiperploskev za opis žikalnih fenomenov, njihovih glavnih razvrstitev, ter opišemo dva obstoječa teoretična pristopa za raziskovanje singularnih ploskev. V drugem poglavju razvijemo teoretična okvirja in vključimo podroben opis obeh pristopov za primera svetlobnih in časovnih (prostorskih) hiperploskev. V tem poglavju prav tako omenimo možno uporabo obeh teoretskih pristopov za primer, ko hiperploskev vsebuje svetlobni signal s planarno fronto. V končnem poglavju začnemo z razpravo učinkov, ki jih lahko ima singularna svetlobna hiperploskev na ujemanje časovnih (prostorskih) geodetskih črt. Tu prikažemo nov pristop k izračunu in predstavimo razširitev teorije za primer ujemanja ničelnih geodetskih črt. Na koncu poglavja prikažemo konkretni primer in njegove podobnosti s primeri časovnih geodetskih črt. Z magistersko nalogo tako predlagamo uporabo novega matematičnega okvirja za opis ujemanja ničelnih geodetskih črt, ki prečkajo singularno ničelno hiperploskev. Rezultate, ki jih pri tem prejmemo, je možno uporabiti pri eksperimentalni ziki za detekcijo impulznih signalov, ki se nahajajo v singularnih ničelnih hiperploskvah. Kot primer opišemo lastnosti in možnosti detektorja impulznih svetlobnih signalov, ki vključujejo gravitacijske valove.
Keywords:singularna hiperploskev, impulzni signal, gravitacijski val, ničelna geodetska črta, časovna (prostorska) geodetska črta


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