Prostorno-vremenski singulariteti

master's thesis

• Title (english): Space-time singularities
• Author: Mateo Paulišić
• Mentor: Ivica Smolić (mentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Mirko Planinić (član povjerenstva)
• Committee member: Vernesa Smolčić (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2016-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Već je prvo egzaktno riješenje Einsteinovih jednadžbi pokazalo divergiraju će ponašanje metrike za neke vrijednosti svojih parametara. Iako je bilo potrebno nekoliko desetljeća da bi analiza pokazala koje su divergencije "prave" a koje samo artefakt koordinatnog sustava, naznaka singulariteta bila je prisutna. U ovom radu definiramo singularitete, na konkretnom primjeru pokazujemo kako dana definicija funkcionira i uvodimo veliku paletu alata kojima je moguće analizirati strukturu prostor-vremena bez ulaženja u detalje konkretnih rješenja. Konačno, prezentiramo, propitujemo i dokazujemo jedan od najvažnijih teorema o singularitetima (Hawking, Penrose 1970.) koji nam uz određena opravdanja daje indikacije da je i naše prostor-vrijeme singularno.

Abstract (english)

The first ever exact solution of Einstein field equations already gave a glimpse of a phenomenon later to be called a singularity. In this work, we will present a carefully motivated definition of singularities, show how it can be used on one of the known exact solutions and then move on to enquiring how often singularities are among non-special space-times. We will introduce a plethora of tools for analyzing models of space-times, investigate their properties, and finally, put them to use in examining and proving one of the most important singularity theorems in the 20th century (Hawking, Penrose 1970). Along with physics-motivated arguments, this theorem will give us an argument to believe that our space-time is also singular.

• Keywords: prostorno-vremenski singulariteti
• Keywords (english): space-time singularities
• Language: croatian
• URN:NBN: urn:nbn:hr:217:738463
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-03-04 17:17:48