Geometrijske nejednakosti u općoj teoriji relativnosti

master's thesis

• Title (english): Geometric inequalities in general relativity
• Author: Mate Picukarić
• Mentor: Ivica Smolić (mentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Krešimir Kumerički (član povjerenstva)
• Committee member: Emil Tafra (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2020-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Kod Kerr-Newmanovog rješenja Einsteinove jednadžbe masa, angularni moment i naboj zadovoljavaju određene nejednakosti. Dotične nejednakosti usko su povezane s pretpostavkom kozmičke cenzure te ih je moguće primjeniti i na dinamičke crne rupe zbog čega je njihovo proučavanje toliko interesantno. Jedna od takvih nejednakosti je teorem o pozitivnosti mase. U ovom radu izložit ćemo Wittenov dokaz teorema o pozitivnosti mase i uvesti alate potrebne za njegovo razumijevanje. Osim toga, pobliže ćemo objasniti pojam geometrijskih nejednakosti, navesti primjere i motivaciju iza proučavanja takvih nejednakosti kao i suvremene rezultate te neriješene probleme.

Abstract (english)

In Kerr-Newman’s solution of Einstein’s equation, mass, angular momentum and charge satisfy certain inequalities. These inequalities are closly related with the cosmic censorship conjecture which makes them particularly interesting to study. One such inequality is the positive mass theorem. In this work we will studyWitten’s proof of the positive mass theorem and introduce tools required for it’s understanding. We will also explain the meaning of geometric inequalities, present examples and motivation behind their studying, and list some current results and open problems in this subject.

• Keywords: opća teorija relativnosti; geometrijske nejednakosti; izoperimetrijska nejednakost; hipoteza kozmičke cenzure; energijski uvjeti; ADM masa; spinori; Wittenov dokaz
• Keywords (english): general relativity; geometric inequalities; isoperimetric inequality; cosmic censorship conjecture; energy conditions; ADM mass; spinors; Witten’s proof
• Language: croatian
• URN:NBN: urn:nbn:hr:217:130887
• 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: 2021-01-08 12:16:27