From Black Holes to Wormholes in Higher Spin Gravity
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Typ
Examensarbete för kandidatexamen
Bachelor Thesis
Bachelor Thesis
Program
Publicerad
2017
Författare
Ekhammar, Simon
Erkensten, Daniel
Lassila, Marcus
Nilsson, Torbjörn
Modellbyggare
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Volymtitel
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Sammanfattning
The recent ER=EPR conjecture as well as advances in string theory have spurred the interest in wormholes and their relation to black holes. The complexity of these phenomena motivates the restriction to a tensionless limit of string theory, which is believed to be described by a higher spin theory. This thesis investigates the specific case of three-dimensional black holes and wormholes in Einstein- and higher spin gravity. We first study black holes and wormholes in general relativity, and it is found that to have traversable wormholes we must introduce exotic matter, i.e. matter with negative energy density. It is then shown that the Einstein-Hilbert action in 2+1 dimensions can be expressed as a Chern-Simons action with the gauge group SL(2) × SL(2). By extending the gauge group to SL(3) × SL(3) a generalization of Einstein gravity is obtained, yielding a higher spin gravity theory. In the extended theory the metric, which was previously fundamental, has become gauge dependent. Because of this we must instead classify solutions through the holonomy. We show that in this theory we can resolve a conical singularity without changing its holonomy. What is more interesting, is that we show that this precise transformation transforms both the cone and the black hole to a traversable wormhole. Of course, this possibility brings into question the interpretation of matter, and more fundamentally, the stress-energy tensor in a higher spin gravity theory. Even without fully resolving these issues the theory can be useful, as it provides a possible way of simplifying calculations by changing the geometry of a problem without changing its solution. As this text is geared towards undergraduates in physics, it begins with an introductory chapter on Maxwell’s theory of electromagnetism as it is an example of what might possibly be the simplest gauge theory. Generalizing this theory to non-abelian groups leads to Yang-Mills and Chern-Simons theories. An introduction to general relativity with a special emphasis on the Cartan formulation, is provided as well. In addition to this there are multiple appendices detailing the necessary mathematical background needed to understand the later parts of the work.
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Building Futures , Energi , Materialvetenskap , Grundläggande vetenskaper , Hållbar utveckling , Innovation och entreprenörskap (nyttiggörande) , Annan naturvetenskap , Building Futures , Energy , Materials Science , Basic Sciences , Sustainable Development , Innovation & Entrepreneurship , Other Natural Sciences