|
|
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)
|
|
|
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
|
|
|
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.
|
|
|
Selected problems in relativistic cosmology
Kerachian, Morteza ; Bičák, Jiří (advisor) ; Balek, Vladimír (referee) ; Vikman, Alexander (referee)
In this work, we studied three selected problems in FRW spacetime. In the first part, we analysed the motion of a test particle in the homogeneous and isotropic universe. We presented a framework in which one can derive the uniformly accelerated trajectory and geodesic motion if a scale factor for a given spacetime is provided as a function of coordinate time. By applying the confomal time transformation, we were able to convert second order differential equations of motion in FRW spacetime to first order differential equations. From this, we managed to obtain a formalism to derive the uniformly accelerated trajectory of a test particle in spatially curved FRW spacetime. The second part of this work is devoted to dynamical cosmology. In particular, we analyse the cases of barotropic fluids and non-minimally coupled scalar field in spatially curved FRW spacetime. First, we set up the dynamical systems for an unspecified EoS of a barotropic fluid case and an unspecified positive potential for a non-minimal coupled scalar field case. For both of these systems, we determined well-defined dynamical variables valid for all curvatures. In the framework of these general setups we discovered several characteristic features of the systems, such as invariant subsets, symmetries, critical points and their...
|
|
|
Dynamical analysis approaches in spatially curved FRW spacetimes
Kerachian, M. ; Acquaviva, G. ; Lukes-Gerakopoulos, Georgios
We summarize two agnostic approaches in the framework of spatially curved Friedmann-Robertson-Walker (FRW) cosmologies discussed in detail in (Kerachian et al., 2020, 2019). The first case concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS), for which the only assumption made is the non-negativity of the fluid’s energy density. The second case concerns the dynamics of a non-minimally coupled real scalar field with unspecified positive potential. For each of these models, we define a new set of dimensionless variables and a new evolution parameter. In the framework of these agnostic setups, we are able to identify several general features, like symmetries, invariant subsetsand critical points, and provide their cosmological interpretation.
|
|
|
Chaos in deformed black-hole fields
Witzany, Vojtěch ; Semerák, Oldřich (advisor) ; Kopáček, Ondřej (referee)
The consequences of two key approximations of accretion-disc physics near black holes are studied in this thesis. First, the question of effective ``pseudo-Newtonian" potentials mimicking a black hole is investigated both through numerical simulations and analytical means, and second, the neglect of additional gravitating matter near accreted-upon black holes and its consequences are put to test. After some broader discussion of integrability, resonance and chaos, a general "pseudo-Newtonian" limit for geodesic motion is derived, and applied for the case of null geodesics near a glowing toroid and for time-like geodesics in the Kerr metric. Afterwards, a new Newtonian gravitational potential for non- singular toroids is proposed and its usefulness for the so-called Weyl space-times is discussed. Finally, a new pseudo-Newtonian potential is introduced and applied alongside already known potentials in models of free test particle motion in the field of a black hole with a disc or ring, in complete analogy with previous exact-relativistic studies, and the previous conclusion of chaos in disc/ring-hole models is confirmed. Overall, the pseudo-Newtonian framework is able to reproduce a number of key features of the original systems with notable differences arising only as a consequence of extremely strong or...
|
|
|
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)
|
|
|
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.
|
|
|
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
|
|
|
Physical and astronomical discussions
Oupický, Pavel
Paper is oriented on the problem parts of physic and astronomy .\nLast year I tried a few considerations about the physical astronomical problems (the FAU I.) in which I did not have a clear or vice versa, I think that they clearly have .. in anything but I'm not too sure, especially with some of the problems was clear to me that some of my comments may be next as they say .. and it was one of the motivations that led me to this sequel .. something i will continue here, something correct and perhaps in between appear as something new and interesting. This time I am going to deal with the following areas of concern of physics and astronomy.
|
guest ::
