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Gravitational wave templates from Extreme Mass Ratio Inspirals
Skoupý, Viktor ; Loukes Gerakopoulos, Georgios (advisor) ; van de Meent, Maarten (referee) ; Wardell, Barry (referee)
Future space-based gravitational-wave detectors will require highly accurate gravi- tational wave templates for detecting extreme mass ratio inspirals and estimating their parameters. These templates must include the postadiabatic effects like the spin of the secondary body. Therefore, we investigate the influence of the secondary spin on the motion around a Kerr black hole, calculate the corresponding gravitational-wave fluxes to produce flux-driven inspirals and reveal the shifts of the gravitational-wave phases induced by the secondary's spin. In particular, this study begins by considering eccentric equatorial orbits, where we obtain the constants of motion and fundamental frequen- cies using the Mathisson-Papapetrou-Dixon equations. Next, we derive the linear-in-spin parts of these quantities. We introduce a new Teukolsky equation solver in the frequency domain to calculate the energy and angular momentum fluxes from these trajectories. We use the obtained fluxes to adiabatically evolve the orbital parameters and to find the spin-induced phase shifts. For off-equatorial orbits, a frequency-domain approach is employed to determine the trajectories in the linear-in-spin regime and to compute the re- spective fluxes. The agreement between the frequency-domain fluxes and those acquired using an existing...
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Dynamic elektromagnetic fields in the Kerr spacetime
Skoupý, Viktor ; Ledvinka, Tomáš (advisor) ; Kofroň, David (referee)
In this thesis we study a test electromagnetic field in the vicinity of Kerr black hole and with methods of extraction of its rotational energy. We are investigating a process in which a particle moves in an electromagnetic resonator around Kerr black hole. The energy of the particle is transferred to the electromagnetic field and the particle falls into the black hole with negative energy. We begin with the derivation of Maxwell's and Teukolsky equations and their numerical solutions. We derive a boundary condition for an electromagnetic field on a spherical mirror around the black hole, find the field that satisfies this condition, and describe the procedure for numerical calculation. Next, we calculate the trajectories of charged test particles in such a field and find particles that fall into the black hole with negative energy. We have found that it is possible for the particle to fall into the black hole with the energy of −124% of its rest mass, and the parameters of the electromagnetic field and trajectory of the particle need to be carefully selected.
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Kinematics of particle collisions in the ergosphere of Kerr black hole
Skoupý, Viktor ; Ledvinka, Tomáš (advisor) ; Žofka, Martin (referee)
In the thesis we deal with an effect which can be used to extract energy from a rotating black hole, so-called collisional Penrose process. First we investigate the ways to find the equations of motion in the general relativity using Hamilto- nian. Then we examine the equations of motion and their consequences in several coordinate systems for the space-time in the vicinity of a rotating black hole. Fi- nally we look into ways to create a particle capable to escape to infinity with as big energy as possible using Compton scattering and annihilation. The biggest energy found is approximately 14 times the energy of the incoming particles. The efficiency decreases with the distance from the horizon and with the decreasing specific angular momentum of the black hole. 1
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