Teleparalelna gravitacija

master's thesis

• Title (english): Teleparallel gravitation
• Author: Luka Benić
• Mentor: Ivica Smolić (mentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Petar Žugec (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Committee member: Vernesa Smolčić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2023-09-19, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Opća teorija relativnosti, kao klasična teorija gravitacije, bazira se na jedinstvenoj Levi-Civitinoj koneksiji, koja je u potpunosti određena metričkim tenzorom dane glatke mnogostrukosti. Jedinstvenost Levi-Civitine koneksije temelji se na pretpostavkama iščezavajućeg tenzora torzije i kompatibilnosti metrike s kovarijantnom derivacijom, odnosno iščezavajućeg tenzora nemetričnosti. Posljedično u takvom formalizmu gravitacija je u potpunosti opisana svojstvima Riemannovog tenzora zakrivjenosti, odnosno zakrivljenošću promatranog prostorvremena. U ovom radu razmotramo posljedice popuštanja navedenih pretpostavki te dolazimo do zaključka da postoji dinamička ekvivalentnost opće teorije relativnosti s teorijama koje se temelje na iščezavanju Riemannovog tenzora zakrivljenosti, a na neiščezavanju ili istovremeno tenzora torzije i tenzora nemetričnosti ili na neiščezavanju samo tenzora nemestričnosti ili na neiščezavanju samo tenzora torzije. Također pokazujemo da u ovakvom formalizmu postoji mogućnost promatranja klasične gravitacije kao baždarne teorije bazirane na Liejevoj grupi translacija. Nadalje, promatramo pripadne modificirane teorije gravitacije te pokazujemo da time dolazimo do novih dinamičkih modela, koji se općenito razlikuju od dinamičkih modela dobivenih modificiranim teorijama opće teorije relativnosti. Tako dobiveni dinamički modeli su intenzivan predmet istraživanja, naročito u kozmološkim modelima.

Abstract (english)

The general theory of relativity, as a classical theory of gravitation, is based on a unique Levi-Civita connection, which is entirely given by the metric tensor of a given smooth manifold. The uniqueness of the Levi-Civita connection is based on the assumptions of vanishing torsion tensor and compatibility of the metric with the covariant derivative, or in other words vanishing non-metricity tensor. As a consequence of this formalism, gravitation is entirely given by the properties of the Riemann curvature tensor, or with the curvature of a given spacetime. In this text, we are exploring the consequences of relaxing the aforementioned assumptions and we conclude that there exists a dynamical equivalence between the general theory of relativity with theories based on a vanishing Riemann curvature tensor, and simultaneously nonvanishing torsion and non-metricity tensors, or with only non-metricity as a nonvanishing tensor, or with only torsion as a nonvanishing tensor. We also show that in this formalism there is a possibility of treating classical gravitation as a gauge theory based on the Lie group of translations. Furthermore, we look at given modified theories of gravitation in this formalism and we see that we end up with new dynamical models, which are in general different from dynamical models obtained from modified theories of the general theory of relativity. Those dynamical models are the subject of intense research, especially in the cosmological models.

• Keywords: Riemannova geometrija; opća teorija relativnosti; teleparalelne geometrije; teleparalelne gravitacije; baždarenje gravitacije
• Keywords (english): Riemannian geometry; general theory of relativity; teleparallel geometries; teleparallel gravitations; gauging of gravitation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:145800
• 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: 2023-11-21 13:24:01