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Rotating thin disc around a Schwarzschild black hole: properties of perturbative solution
Kotlařík, Petr ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee)
In 1974, Will presented a solution for the perturbation of a Schwarzschild black hole due to a slowly rotating and light thin disc given in terms of a multipole expansion of the perturbation series. In a recently submitted paper, P. Čížek and O. Semerák generalized this procedure to the perturbation by a slowly rotating finite thin disc, using closed forms of Green functions rather than the multipole expansion. The method is illustrated there, in the first perturbation order, on the constant-density disc. In this thesis, we summarize, check and plot some of the obtained properties, and show how the presence of the disc changes the geometry of a horizon and the position of significant circular orbits. 1
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Black holes under the influence of strong sources of gravitation
Kotlařík, Petr ; Semerák, Oldřich (advisor) ; Kofroň, David (referee)
In this thesis we study a deformation of a black-hole spacetime due to another strong sources of gravity. Keeping within static and axially symmetric metrics, we consider a binary of Schwarzschild black holes held apart from each other by a repulsive effect of an Appell ring. After verifying that such a system can rest in static equilibrium (without any supporting struts), we compute its several basic geometric characteristics and we plot simple invariants determined by the metric functions (especially lapse, or, equivalently, potential) and by their first and second derivatives (gravitational acceleration and Kretschmann scalar). Then we extend the analysis below the black-hole horizon and inspect the behaviour of the scalars inside. The geometry turns out to be deformed in a non-trivial way, we even find regions of negative Kretschmann scalar in some cases. In the second part, we present a summary of the perturbative solution describing a slowly rotating system of a black hole surrounded by a thin finite circular disc, and an analysis of equatorial circular geodesics in such a spacetime. 1
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Rotating thin disc around a Schwarzschild black hole: properties of perturbative solution
Kotlařík, Petr ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee)
In 1974, Will presented a solution for the perturbation of a Schwarzschild black hole due to a slowly rotating and light thin disc given in terms of a multipole expansion of the perturbation series. In a recently submitted paper, P. Čížek and O. Semerák generalized this procedure to the perturbation by a slowly rotating finite thin disc, using closed forms of Green functions rather than the multipole expansion. The method is illustrated there, in the first perturbation order, on the constant-density disc. In this thesis, we summarize, check and plot some of the obtained properties, and show how the presence of the disc changes the geometry of a horizon and the position of significant circular orbits. 1
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