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General Relativity in Higher Dimensions
Málek, Tomáš ; Pravda, Vojtěch (advisor) ; Raeymaekers, Joris (referee) ; Podolský, Jiří (referee)
vii Title: General relativity in higher dimensions Author: Tomáš Málek Institute: Institute of Theoretical Physics Supervisor: Mgr. Vojtěch Pravda, PhD., Institute of Mathematics of the Academy of Sciences of the Czech Republic Abstract: In the first part of this thesis, Kerr-Schild metrics and extended Kerr- Schild metrics are analyzed in the context of higher dimensional general relativ- ity. Employing the higher dimensional generalizations of the Newman-Penrose formalism and the algebraic classification of spacetimes based on the existence and multiplicity of Weyl aligned null directions, we establish various geometri- cal properties of the Kerr-Schild congruences, determine compatible Weyl types and in the expanding case discuss the presence of curvature singularities. We also present known exact solutions admitting these Kerr-Schild forms and con- struct some new ones using the Brinkmann warp product. In the second part, the influence of quantum corrections consisting of quadratic curvature invariants on the Einstein-Hilbert action is considered and exact vacuum solutions of these quadratic gravities are studied in arbitrary dimension. We investigate classes of Einstein spacetimes and spacetimes with a null radiation term in the Ricci tensor satisfying the vacuum field equations of quadratic gravity...
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Higher spin theories in three dimensions
Flandera, Aleš ; Raeymaekers, Joris (advisor) ; Procházka, Tomáš (referee)
In this thesis the theory of general relativity is rewritten into a gauge Chern- Simons theory. The vielbein formalism is used for this purpose. It is shown that the action of such a theory corresponds to the Einstein-Hilbert action. The most important properties of the Chern-Simons theory are investigated. However the aim is to extend this description of spin-2 particles to the higher spin ones. This is done through treating Lie algebra generators and their potentials. Properties of the spin-2 solution are discussed in this context. An example of higher spin solutions, so-called conical defects, is also given.
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General Relativity in Higher Dimensions
Málek, Tomáš ; Pravda, Vojtěch (advisor) ; Raeymaekers, Joris (referee) ; Podolský, Jiří (referee)
vii Title: General relativity in higher dimensions Author: Tomáš Málek Institute: Institute of Theoretical Physics Supervisor: Mgr. Vojtěch Pravda, PhD., Institute of Mathematics of the Academy of Sciences of the Czech Republic Abstract: In the first part of this thesis, Kerr-Schild metrics and extended Kerr- Schild metrics are analyzed in the context of higher dimensional general relativ- ity. Employing the higher dimensional generalizations of the Newman-Penrose formalism and the algebraic classification of spacetimes based on the existence and multiplicity of Weyl aligned null directions, we establish various geometri- cal properties of the Kerr-Schild congruences, determine compatible Weyl types and in the expanding case discuss the presence of curvature singularities. We also present known exact solutions admitting these Kerr-Schild forms and con- struct some new ones using the Brinkmann warp product. In the second part, the influence of quantum corrections consisting of quadratic curvature invariants on the Einstein-Hilbert action is considered and exact vacuum solutions of these quadratic gravities are studied in arbitrary dimension. We investigate classes of Einstein spacetimes and spacetimes with a null radiation term in the Ricci tensor satisfying the vacuum field equations of quadratic gravity...
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