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Generating Methods in GR and Properties of the Resulting Solutions
Hruška, Jakub ; Žofka, Martin (advisor) ; Pravdová, Alena (referee) ; Gürlebeck, Norman (referee)
The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1
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Generating Methods in GR and Properties of the Resulting Solutions
Hruška, Jakub
The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1
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Investigation of chaotic dynamical systems using the methods of Riemannian geometry
Matejov, Dávid ; Scholtz, Martin (advisor) ; Ledvinka, Tomáš (referee)
In this thesis we investigate a chaos in dynamical systems described by the Hamilton function using a new geometric method. At first, necessary definitions and terms are introduced, like dynamical systems, Lyapunov ex- ponents and Poncaré sections. Subsequently we deal with the new geometric method (Horowitz et al., 2007), which predicts the stability of a system un- der consideration. An extensive part is devoted to the general relativity and spinor formalism, the Newman-Penrose formalism and the theory of optical scalars. In the computational part of the thesis, we investigate the pp-waves and chaotic behaviour of geodesics in this class of space-times. All calcula- tions are done in the Python programming language, so we the chapter on numerical calculations is included. 1
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Generating Methods in GR and Properties of the Resulting Solutions
Hruška, Jakub
The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1
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Generating Methods in GR and Properties of the Resulting Solutions
Hruška, Jakub ; Žofka, Martin (advisor) ; Pravdová, Alena (referee) ; Gürlebeck, Norman (referee)
The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1
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