Non-relativistic gravity theories and their relations to multi-metric theories

dc.contributor.advisor Kahya, Emre Onur
dc.contributor.author Şenışık, Cemal Berfu
dc.contributor.authorID 770975
dc.contributor.department Physics Engineering Programme
dc.date.accessioned 2025-04-21T12:14:45Z
dc.date.available 2025-04-21T12:14:45Z
dc.date.issued 2022
dc.description Thesis (M.Sc.) -- İstanbul Technical University, Graduate School, 2022
dc.description.abstract Lie algebra expansion is an exciting method to obtain higher dimensional algebras and using this method one can write some interesting non-relativistic gravitational theories beginning from the Poincaré algebra. This method was first developed by Hatsuda and Sakaguchi (2003) and has been used in many other studies. In this work, we will first give a brief introduction to the gauge theories, which are seminal for understanding gravitational theories in depth, especially the algebraic structure of gravitational theories. Note that this is crucial for many gravity theories, such as supergravity. After that, we will study the general aspects of differential geometry shortly. This will give us the main mathematical framework to study gravity as a gauge theory. Thirdly, we will try to understand the theories of gravity, especially general relativity, as a gauge theory. After a simple introduction to the second-order formalism of GR, we will define the first-order formalism and its action. In the last part of this section, we will obtain GR beginning from the Poincaré algebra and by gauging this algebra. At last, we will give the definition of Newton-Cartan theory, its conditions, and its action. We will first show that this theory can be obtained from an algebraic point of view, i.e. by using Lie Algebra Expansion. We will also give the method, which is based on Ekiz et al. (2022), to obtain the same results by contraction of a multi-metric theory.
dc.description.degree M.Sc.
dc.identifier.uri http://hdl.handle.net/11527/26877
dc.language.iso en
dc.publisher Graduate School
dc.sdg.type Goal 9: Industry, Innovation and Infrastructure
dc.subject Lie algebra
dc.subject non-relativistic gravitational theories
dc.subject Gauge theories
dc.subject gravity theories
dc.subject supergravity
dc.subject differential geometry
dc.title Non-relativistic gravity theories and their relations to multi-metric theories
dc.title.alternative Göreli olmayan kütleçekim teorileri ve çok metrikli teorilerle ilişkileri
dc.type Master Thesis
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