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The wave equation and redshift in Bianchi type I spacetimes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Vågekvationen och rödförskjutning i Bianchi typ I rumtider. (Swedish)
Abstract [en]

The thesis consists of two independent parts. In the first part, we show how the solution to the scalar wave equation on 3-torus-Bianchi type I spacetimes can be written as a Fourier decomposition. We present results on the behaviour of these Fourier modes and apply them to the case of 3-torus-Kasner spacetimes. In the second part, we first consider the solution to the scalar wave equation, with special initial data, as a model for light in Bianchi type I spacetimes. We show that the obtained redshift coincides with the cosmological redshift. We also consider the Cauchy problem for Maxwell's vacuum equations, with special initial data, in order to model light in Bianchi type I spacetimes. We calculate the redshift of the solution and show that, also in this case, the obtained redshift coincides with the cosmological redshift.

Abstract [sv]

Uppsatsen består av två oberoende delar. I den första delen visar vi hur lösningen till den skalära vågekvationen i Bianchi typ I rumtider med 3-torus topologi kan skrivas som en Fourierserie med tidsberoende koefficienter, så kallade moder. Vi presenterar resultat som beskriver egenskaper hos dessa moder och applicerar resultaten i specialfallet med Kasner rumtider med 3-torus topologi. I den andra delen betraktar vi först lösningar till den skalära vågekvationen, med speciella initialdata, som en modell för ljus i Bianchi typ I rumtider. Vi visar att rödförskjutningen på ljuset sammanfaller med den kosmologiska rödförskjutningen i Bianchi typ I rumtider. Därefter betraktar vi Cauchyproblemet för Maxwells vakuumekvationer, med speciella initialdata, som en annan modell för ljus i Bianchi typ I rumtider. Vi beräknar rödförskjutningen på ljuset med denna modell och visar att, även i detta fall, sammanfaller den med den kosmologiska rödförskjutningen.

Place, publisher, year, edition, pages
2014.
Series
TRITA-MAT-E, 2014:57
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-151317OAI: oai:DiVA.org:kth-151317DiVA: diva2:754277
External cooperation
University of Potsdam, Germany
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2014-10-10 Created: 2014-09-17 Last updated: 2014-11-12Bibliographically approved

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