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Slowly rotating sources around static black holes
Čížek, Pavel ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee)
In this thesis we study the possibility of perturbative solution of the Einstein equations in the case of stationary and axially symmetric metric. The method is motivated by the pursuit of describing the astrophysically important system of a black hole surrounded by a thin disc or a ring. A Schwarzschild black hole is thus considered as a central source, with a light and/or slowly rotating disc around. We show that the metric can be found in terms of perturbative expansions in relative disc mass or in inverted distance from the hole, and point out where problems occur. The approach can be applied to a disc "given in advance" as well as in the "self-consistent" case when the disc elements orbit on circular geodesics in the desired total eld. It can also be generalised to the discs composed of more dust components.
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Thin discs and rings as sources of Weyl space-times
Kubíček, Jan ; Semerák, Oldřich (advisor) ; Žofka, Martin (referee)
Static and axially symmetric vacuum solutions of Einstein's equations can be descri- bed by the Weyl metric which only depends on two unknown functions, given by the Laplace equation and a line integral. In this thesis we study some properties of two Weyl space-times whose sources are one-dimensional rings - the Appell ring and the Bach-Weyl ring. On the behaviour of proper distances and geodesics in the central region we demonstrate that in Weyl coordinates these sources represent directional singularities. 1
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Chaos in motion around black holes
Suková, Petra ; Semerák, Oldřich (advisor) ; Šubr, Ladislav (referee)
The geodesic motion around Kerr black holes is regular, but this may change when an additional source is present, even if the space-time symmetry were not lowered. In this thesis we study the eect of a simple (static and axially symmetric) additional source on geodesic dynamics in the eld of a Schwarzschild black hole. In the static case the complete space-time can be described by an exact solution of Einstein equations thanks to a relatively simple superposition of the central-black-hole and the external-source metrics. Following the astrophysical motivation, we will specically consider, as the external source, the thin ring (linear source) of the Bach-Weyl type and innite thin discs (planar sources) of several types (inverted counter-rotating discs of Morgan and Morgan and the discs with power-law radial shape of density). The results may be relevant e.g. for a long-term behaviour of discrete sources (stars) in the eld of a very massive black hole in a galactic nucleus, surrounded by an accretion disc and/or by a massive toroid.
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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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Astrofyzikální procesy v blízkosti kompaktních objektů
Sochora, Vjačeslav ; Karas, Vladimír (advisor) ; Schee, Jan (referee) ; Semerák, Oldřich (referee)
Title: Astrophysical processes near compact objects: studying extremal en- ergy shifts from accretion rings Author: Vjačeslav Sochora Department: Academy of Sciences of the Czech Republic, Astronomical In- stitute Supervisor: doc. RNDr. Vladimír Karas, DrSc.; Academy of Sciences of the Czech Republic, Astronomical Institute Abstract: The X-ray emission from inner regions of an accretion disk around black holes provides wealth of information about matter in extreme con- ditions. A spectral profile of radiation from a narrow circular ring has a characteristic double-horn profile. Red and blue peaks of the profile are close to the extremal values of the energy shift. We describe a useful approach to calculate the extremal energy shifts in the regime of strong gravity. We dis- cuss if the radial structure of the disk emission could be reconstructed using extremal energy shifts of the individual rings. For this purpose, we simulate artificial data from a bright active galactic nucleus and show that the re- quired sensitivity and energy resolution can be reached with the proposed LOFT mission. Keywords: black hole physics, accretion disks, galactic nuclei
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Geodesic chaos in a perturbed Schwarzschild field
Polcar, Lukáš ; Semerák, Oldřich (advisor) ; Kopáček, Ondřej (referee)
We study the dynamics of time-like geodesics in the field of black holes perturbed by a circular ring or disc, restricting to static and axisymmetric class of space-times. Two analytical methods are tested which do not require solving the equations of motion: (i) the so-called geometric criterion of chaos based on eigenvalues of the Riemann tensor, and (ii) the method of Melnikov which detects the chaotic layer arising by break-up of a homoclinic orbit. Predictions of both methods are compared with numerical results in order to learn how accurate and reliable they are.
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Centre of the Kerr and Appell space-times
Jurčík, Róbert ; Semerák, Oldřich (advisor) ; Žofka, Martin (referee)
One of the most important solutions of Einstein equations is the Kerr metric. At the very centre of this space-time, there lies a ring curvature singularity. The singularity encircles a surface which joins together two asymptotically flat sheets of the manifold. The surface is intrinsically flat and is standardly interpreted as a planar disc. However, an article has been recently published which claims that the central surface is actually a dicone, with vertex (vertices) on the symmetry axis. In this thesis we analyse various geometric characteristics of the surface, in order to check which of the pictures is more adequate. We also examine the same surface of the Appell space-time which has the same spatial structure as the Kerr one. 1
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