|
|
Chaos v porušených polích černých děr
Witzany, Vojtěch ; Semerák, Oldřich (advisor) ; Heyrovský, David (referee)
The loss of complete geodesic integrability is one of the important consequences (and thus indicators) of deviation from the Kerr-type space-time. Indeed, it has been confirmed many times in the literature that even a highly symmetric perturbation of the Kerr or Schwarzschild metric can make the free test-particle motion chaotic. In this thesis, we study the test-particle dynamics in the field of a Schwarzschild black hole surrounded by a thin disc or ring, using, however, Newton's gravity with a simple "pseudo- Newtonian" potential to mimic the black hole. The Poincaré sections show that the (pseudo-)Newtonian system is slightly more chaotic than the general relativistic one. The difference seems to be correlated with the phase-space allowed region being more open towards the center in the pseudo-Newtonian case. Powered by TCPDF (www.tcpdf.org)
|
|
|
Geometry inside deformed black holes
Basovník, Marek ; Semerák, Oldřich (advisor) ; Svítek, Otakar (referee)
In this thesis we study exact general relativistic space-times generated by a black hole and an additional source of gravity, while restricting to two classes of static and axially symmetric solutions: the Majumdar-Papapetrou solution for a couple (in general, a multiple system) of extremally charged black holes and the "superposition" of a Schwarzschild black hole with the Bach-Weyl thin ring. We follow the effect of the additional source on the geometry of black-hole space-time on the behaviour of important invariants, in particular of the simplest scalars obtained from the Riemann and possibly also Ricci tensor. We have plotted the invariants both outside and inside the black hole; in the case of a Schwarzschild black hole with ring, we found, to this end, an extension of the metric below the horizon. It turns out that the external source may affect the geometry inside the black hole considerably, even in the vicinity of singularity, although the singularity itself remains point-like in both solutions studied here.
|
|
|
Numerical evolution of black-hole spacetimes
Khirnov, Anton ; Ledvinka, Tomáš (advisor) ; Palenzuela, Carlos (referee)
吀e so-called "trumpet" initial data has recently received mu挀 a琀ention as a potential candidate for the natural black hole initial data to be used in 3+1 numerical relativity simulations with 1+log foliation. In this work we first derive a variant of the maximal trumpet initial data that is made to move on the numerical grid by the means of a Lorentz boost and write a numerical code that constructs this boosted trumpet initial data. We also write a numerical code for calculating the Krets挀mann scalar from the 3+1 variables, to be used in analysing the data from our simulations. With the help of those two codes, we study the behaviour of the boosted trumpet initial data when evolved with the BSSN formulation of the Einstein equations, using 1+log slicing and the Γ-driver shi昀 condition.
|
|
|
Properties of the extreme charged black hole near horizon
Hejda, Filip ; Krtouš, Pavel (advisor) ; Svítek, Otakar (referee)
It is known, that there exists a limiting correspondence between certain part (including the horizon) of extremal case of Reissner-Nordström space-time and Robinson-Bertotti space-time and that different generalisations of this near-horizon limit are possible. The aim of the presented work is to examine some of the properties of such limiting transitions. Firstly it is stressed how the global structure is reflected in the limit and secondly which properties of the space-time do provide that physical distances are preserved in the limit. Besides the extremal case the subextremal and hyperextremal generalisations are studied. As a complementary topic, the global extremal limit is stated. That means a transition from a generalised (non-symmetrical) conformal diagram of the subextremal case to the conformal diagram of the extremal case of Reissner-Nordström solution.
|
|
|
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
|
|
|
Polarisation of X-ray emission from accretion discs in active galactic nuclei
Podgorný, Jakub ; Dovčiak, Michal (advisor) ; Marin, Frédéric (referee)
The presented thesis deals with theoretical modeling of the X-ray emission from active galactic nuclei. It studies spectral and polarisation properties of local radiation reflected from the surrounding accretion disc, which is being illuminated by a hot corona above, as well as global observational perspectives at infinity for unobscured radio-quiet sources. Modeling of this kind could then serve for observational fitting of spin of the central supermassive black hole, constraining the accretion disc's or coronal properties, or de- termining observer's inclination towards the systems. A radiative transfer Monte Carlo simulation code STOKES [Goosmann and Gaskell, 2007, Marin et al., 2012, 2015, Marin, 2018] is used for local computations. Its performance is compared to results of other attempts already existing in literature and analytical approximations. The local scheme is discussed mostly in terms of emergent polarisation that has been for the first time simulated for these types of objects with high accuracy. Integration over the accretion disc and superposition with the primary radiation in the so-called lamp-post or extended coronal model, including all general relativistic effects in the vicinity of the central super- massive black hole, is then performed on the basis of already existing routine...
|
|
|
Polarisation of X-ray emission from accretion discs in active galactic nuclei
Podgorný, Jakub ; Dovčiak, Michal (advisor)
The presented thesis deals with theoretical modeling of the X-ray emission from active galactic nuclei. It studies spectral and polarisation properties of local radiation reflected from the surrounding accretion disc, which is being illuminated by a hot corona above, as well as global observational perspectives at infinity for unobscured radio-quiet sources. Modeling of this kind could then serve for observational fitting of spin of the central supermassive black hole, constraining the accretion disc's or coronal properties, or de- termining observer's inclination towards the systems. A radiative transfer Monte Carlo simulation code STOKES [Goosmann and Gaskell, 2007, Marin et al., 2012, 2015, Marin, 2018] is used for local computations. Its performance is compared to results of other attempts already existing in literature and analytical approximations. The local scheme is discussed mostly in terms of emergent polarisation that has been for the first time simulated for these types of objects with high accuracy. Integration over the accretion disc and superposition with the primary radiation in the so-called lamp-post or extended coronal model, including all general relativistic effects in the vicinity of the central super- massive black hole, is then performed on the basis of already existing routine...
|
|
|
Polarisation of X-ray emission from accretion discs in active galactic nuclei
Podgorný, Jakub ; Dovčiak, Michal (advisor) ; Marin, Frédéric (referee)
The presented thesis deals with theoretical modeling of the X-ray emission from active galactic nuclei. It studies spectral and polarisation properties of local radiation reflected from the surrounding accretion disc, which is being illuminated by a hot corona above, as well as global observational perspectives at infinity for unobscured radio-quiet sources. Modeling of this kind could then serve for observational fitting of spin of the central supermassive black hole, constraining the accretion disc's or coronal properties, or de- termining observer's inclination towards the systems. A radiative transfer Monte Carlo simulation code STOKES [Goosmann and Gaskell, 2007, Marin et al., 2012, 2015, Marin, 2018] is used for local computations. Its performance is compared to results of other attempts already existing in literature and analytical approximations. The local scheme is discussed mostly in terms of emergent polarisation that has been for the first time simulated for these types of objects with high accuracy. Integration over the accretion disc and superposition with the primary radiation in the so-called lamp-post or extended coronal model, including all general relativistic effects in the vicinity of the central super- massive black hole, is then performed on the basis of already existing routine...
|
|
|
The fields of current loops around black holes
Vlasáková, Zuzana ; Semerák, Oldřich (advisor) ; Karas, Vladimír (referee)
The field of a test current loop placed symmetrically in the equatorial plane around a Kerr black hole has been studied several times and solutions have been published in different forms. We compare these results and determine their limits in important places - in radial infinity, on the outer event horizon, on the static limit, in the equatorial plane and on the axis of symmetry. Furthermore, we show the behaviour of the field corresponding to the extreme black hole and verify Meissner effect. In the end we determine the field of a simple model of a current disc by a superposition of test current loops. This problem has an astrophysical motivation - the description of accretion discs in the vicinity of black holes. 1
|
|
|
Dynamics of spinning test particles in curved spacetimes
Zelenka, Ondřej ; Loukes Gerakopoulos, Georgios (advisor) ; Witzany, Vojtěch (referee)
The motion of a test particle in the Schwarzschild background models the merger of a compact object binary with extremely different masses known in the literature as Extreme Mass Ratio Inspiral. In the simplest geodesic approxima- tion, this motion is integrable and there is no chaos. When one takes the spin of the smaller body into account, integrability is broken and prolonged resonances along with chaotic orbits appear. By employing the methods of Poincaré surface of section, rotation number and recurrence analysis we show for the first time that there is chaos for astrophysically relevant spin values. We propose a uni- versal method of measuring widths of resonances in perturbations of geodesic motion in the Schwarzschild spacetime using action-angle-like variables. We ap- ply this novel method to demonstrate that one of the most prominent resonances is driven by second order in spin terms by studying its growth, supporting the expectation that chaos will not play a dominant role in Extreme Mass Ratio Inspirals. Last but not least, we compute gravitational waveforms in the time- domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source. 1
|
guest ::
