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Weyl metrics and their generalizations: classical and quantum viewpoint
Polcar, Lukáš ; Svítek, Otakar (advisor) ; Ledvinka, Tomáš (referee) ; Pound, Adam (referee)
In this thesis, we study two distinct topics both connected to stationary axially sym- metric spacetimes. The first is a study of an exact solution sourced by phantom scalar field. This solution can be derived from the well-known Curzon-Chazy metric and has several unusual features. It is a spherically symmetric wormhole which is however not symmetric with respect to its throat, it possesses a non-scalar curvature singularity and functions as a one-directional time machine. The energy content of the spacetime is ex- amined and various other properties are discussed. The remaining parts are dedicated to extreme mass ratio inspirals in two stationary axially symmetric spacetimes, perturbed Schwarzschild and Kerr. The canonical perturbation theory was used to transform the respective geodesic Hamiltonian to action-angle coordinates allowing us to evolve flux- driven inspirals in both spacetimes. 1
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Gravitational perturbations in NP/GHP formalism
Pospíšil, Marek ; Kofroň, David (advisor) ; Ledvinka, Tomáš (referee)
This work gets the reader acquainted with tetrad approaches to general theory of re- lativity (GTR), namely with Newman - Penrose (NP) and Geroch - Held - Perose (GHP) formalisms. Obtained expressions are expressed in coordinates. Subsequently, this work concerns with the perturbation techniques in GTR, including both metric perturbation and the method of superpotential, the latter being more common in GHP formalism. Following is the recapitulation of important results based on this method. The core of the work is in generalization of known results for spacetimes with ac- celeration (so called C-metric) and checking previous results using computation in the Wolfram Mathematica program. In order not to work just with rather complicated GHP and NP formalisms, the main result is checked also by transcription into coordinate par- tial derivatives. 1
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Stationary fields in black-hole space-times
Čížek, Pavel ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee) ; Gürlebeck, Norman (referee)
Motivated by modelling of astrophysical black holes surrounded by accretion structures, as well as by theoretical interest, we study two methods how to ob- tain, within stationary and axisymmetric solutions of general relativity, a metric describing the black hole encircled by a thin ring or a disc. The first is a suitable perturbation of a Schwarzschild black hole. Starting from the seminal paper by Will (1974), we showed that it is possible to express the Green functions of the problem in a closed form, which can then be employed to obtain, e.g., a reason- able linear perturbation for a black hole surrounded by a thin finite disc. In the second part we tackle the same problem using the Belinskii-Zakharov generating algorithm, showing/confirming that in a stationary case its outcome is unphysi- cal, yet at least obtaining a modest new result for the (static) "superposition" of a Schwarzschild black hole with the Bach-Weyl ring. 1
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Matter Models in General Relativity with a Decreasing Number of Symmetries
Gürlebeck, Norman ; Bičák, Jiří (advisor) ; Fraundiener, Jörg (referee) ; Ledvinka, Tomáš (referee)
Title: Matter Models in General Relativity with a Decreasing Number of Sym- metries Author: Norman Gürlebeck Institute: Institute of theoretical physics Supervisor: Prof. RNDr. Jiří Bičák, DrSc., dr.h.c. Abstract: We investigate matter models with different symmetries in general relativity. Among these are thin (massive and massless) shells endowed with charge or dipole densities, dust distributions and rotating perfect fluid solutions. The electromagnetic sources we study are gravitating spherical symmetric condensers (including the implications of the energy conditions) and arbitrary gravitating shells endowed with a general test dipole distribution. For the latter the Israel formalism is extended to cover also general discontinuous tangential components of the electromagnetic test field, i.e., surface dipole densities. The formalism is applied to two examples and used to prove some general properties of dipole distributions. This is followed by a discussion of axially symmetric, stationary rigidly rotating dust with non-vanishing proper volume. The metric in the interior of such a configuration can be determined completely in terms of the mass density along the axis of rotation. The last matter models we consider are non-axially symmetric, stationary and rotating perfect fluid solutions. This is done with a...
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Green's functions for two-center-Coulomb problem
Donoval, Jan ; Čížek, Martin (advisor) ; Ledvinka, Tomáš (referee)
Xa/.ev prace: Greenovy I'unkce Schrodingerovy rovnice pro elektron v poll ilvou bodovych naboju Autor: -Ian Donoval Katedra (usLav): Ustav teoreticke f'y/iky Vedoiiei bakalarske pnicr: RXDr. Martin Cr/ek, Pli.D. e-mail vedouciho: ci/ek (_imbox.troja.niff.cmii.c7 Ahsl.rakl: V ])i"(jdl()X,ein'' jn'i'u'i .stiuliijiMiic jioliyl) clckt ronu v pull ih'ou hodovych nnboju. V cclr prac-i j^fitoin pfcdpokladanif.' plutnost t-iorii-Ojipcnlicinicrovy aproxi- niacc. VylvDrcnynii irutiirrirkynii proccdiuanii vc I'"urt,ianu ftisfinc bc/rasovou ScliriJdin^ciovu rovnici a hh-dainc tak rticrj;i(! a vlnovr fnnkcc va/aiiycli stayii cli'ktKnni. Prnccdury a])likiiji'in(' na vy]>or(M stayu iontu niolfknltn-rho vodfku a cU'ktronu \ poli protonia. Diskut ujoitu1 iiiterakcni polt'iu ialy. hlavnt"1 s olili'dcin na jcjich inoxiu'1 pou/iti pfi ijori't.a.ni ro/ptylu niitiproUmu na. yoclfku pri Lcrnialnfcli cncr^iic h. Titk1: Green's lunrlions for two-ui'iittT-Cuuloinb probloni Aut.hor: Jail Donuyal Department: Institute of Theoretical Physics Supervisor: RKDr. Martin Ci/.rk, Ph.D. Sviperyisor\ e-mail address: ci/ek^'mbnx.lioja.mlf.cuni.c/ Abstract: In the present work we study the motion of electron in rlie field of two Coulomb centers with making use of the Born Oppenheinier approxima- tion. We have written numerical procedures in...
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Radiation problems of relativistic systems with symmetries
Bohata, Martin ; Bičák, Jiří (advisor) ; Ledvinka, Tomáš (referee)
The thesis deals with system of interacting particles producing eld with helical symmetry within linear theories of scalar and electromagnetic elds in Minkowski spacetime. Advanced and retarded elds are found of a particle on a circular orbit in space - thus moving along a helical trajectory in spacetime. The results are used in a dynamic (self-consistent) two-body problem under the assumption that the interaction between the particles is mediated by both retarded and advanced elds. As a consequence no radiation reaction force arise and the helical symmetry is maintained. The two-body problem of scalar and electromagnetic elds is discussed in a noninertial system in which particles are at rest. In both cases equilibrium conditions are found and the existence and uniqueness of solution is proved. The equilibrium radius is found explicitly in case of two-body electromagnetic problem in an aproximation of small velocities. In the next part the problem is generalized to the case of N particles producing electromagnetic eld with helical symmetry. The existence of equilibrium conguration is proved in general, and the uniqueness is shown in the aproximation of small velocities.
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