Modeli gravitacije u više od 4 dimenzije i ograničenja na njihove parametre pomoću opažanja Event Horizon Telescope-a

master's thesis

• Title (english): Models of gravity in more than 4 dimensions and constraints on their parameters from Event Horizon Telescope observations
• Author: Matej Vugrinec
• Mentor: Maro Cvitan (mentor)
• Committee member: Maro Cvitan (predsjednik povjerenstva)
• Committee member: Ivica Smolić (član povjerenstva)
• Committee member: Vernesa Smolčić (član povjerenstva)
• Committee member: Amon Ilakovac (član povjerenstva)
• Committee member: Vibor Jelić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-10-18, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Modeli gravitacije u više od četiri dimenzije daju efektivno proširenje na teoriju gravitacije kakvu je postulirao Einstein. Pomoću njih je moguće ispitati posljedice koje bi postojanje dodatnih dimenzija ostavilo na naš svemir. U ovom radu bavimo se upravo takvim modelima, s naglaskom na peterodimenzionalnim ”brane-world” modelima. Krećemo od povijesnog razvoja, počevši s Einsteinovom općom teorijom relativnosti i prvih proširenja u više dimenzija, koja se pripisuju Kaluzi i Kleinu i dolazimo do sve modernijih modela u više dimenzija, konkretno Randall-Sundrum modela. Nakon toga, izvodimo efektivne jednadžbe polja koje vrijede u ”brane-world” modelima. Poslije jednadžbi polja, osvrćemo se na anti-de Sitter prostorvremena i formalnije predstavljamo Randall-Sundrum modele. U sljedećih nekoliko poglavlja poslije toga, promatraju se posljedice koje bi postojanje jedne dodatne prostorne dimenzije ostavilo na Newtonov zakon gravitacije, metrike crnih rupa i na kozmologiju. Na kraju, opisujemo kako se opažanja Event Horizon Telescope-a mogu povezati s teorijom iza ”brane-world” modela i pomoću tih opažanja stavljene su neke gornje granice na parametre modela. Isto tako, naglašavamo važnost detekcije gravitacijskih valova pri ograničavanju parametara takvih modela te njihovu važnost u potrazi za novom fizikom.

Abstract (english)

Models of gravity in more than four dimensions offer a way to find an effective theory of gravity beyond the one postulated by Einstein. By using them as toy theories, we can determine the consequences that the existence of extra dimensions would imprint on our universe. This work is devoted to those models, with the emphasis on five dimensional ”brane-world” models. We begin with an overview of history, starting from Einstein’s general relativity and its first modifications which include extra dimensions - credited to Kaluza and Klein, up to Randall-Sundrum models. After that, we derive effective field equations in ”brane-world” models. We then deal with anti-de Sitter spacetimes and formally present Randall-Sundrum models. In the following chapters we explore the consequences of one extra spatial dimension on Newton’s law of gravity, different black hole metrics and on the cosmology. We finally describe how the observations made by the Event Horizon Telescope can be used in conjunction with the theory behind ”brane-world” models and using those observations we constrain some parameters of those models. We also emphasise the importance of detecting gravitational waves and their use in constraining parameters of ”brane-world” models and more generally, their importance in the search for new physics.

• Keywords: gravitacija; dimenzije; ”brane-world” modeli; Randall-Sundrum modeli; crne rupe; kozmologija; Event Horizon Telescope; gravitacijski valovi
• Keywords (english): gravity; dimensions; ”brane-world” models; Randall-Sundrum models; black holes; cosmology; Event Horizon Telescope; gravitational waves
• Language: croatian
• URN:NBN: urn:nbn:hr:217:329395
• 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: 2023-01-18 17:00:17