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Transition from regular to chaotic motion in black hole magnetospheres
Kopáček, Ondřej ; Karas, Vladimír (advisor) ; Kulhánek, Petr (referee) ; Rezzolla, Luciano (referee)
Cosmic black holes can act as agents of particle acceleration. We study properties of a system consisting of a rotating black hole immersed in a large-scale organized magnetic field. Electrically charged particles in the immediate neighborhood of the horizon are influenced by strong gravity acting together with magnetic and induced electric components. We relax several constraints which were often imposed in previous works: the magnetic field does not have to share a common symmetry axis with the spin of the black hole but they can be inclined with respect to each other, thus violating the axial symmetry. Also, the black hole does not have to remain at rest but it can instead perform fast translational motion together with rotation. We demonstrate that the generalization brings new effects. Starting from uniform electro-vacuum fields in the curved spacetime, we find separatrices and identify magnetic neutral points forming in certain circumstances. We suggest that these structures can represent signatures of magnetic reconnection triggered by frame-dragging effects in the ergosphere. We further investigate the motion of charged particles in these black hole magnetospheres. We concentrate on the transition from the regular motion to chaos, and in this context we explore the characteristics of chaos in...
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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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Emergence of magnetic null points in electro-vacuum magnetospheres of compact objects: The case of a plunging neutron star
Kopáček, Ondřej ; Tahamtan, T. ; Karas, Vladimír
We study the possible emergence of magnetic null points which are astrophysically relevant for the processes of magnetic reconnection. While the magnetic reconnection occurs in the presence of plasma and may lead to violent mass ejection, we show here that strong gravitation of the supermassive black hole may actively support the process by suit-ably entangling the field lines even in the electro-vacuum description. In this contribution we further discuss the case of a dipole-type magnetic field of the neutron staron the plunging trajectory to the supermassive black hole. While we have previously shown that given model in principle admits the formation of magnetic null points, here we explore whether and where the null points appear for the astrophysically relevant values of the parameters.
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Mass loss from binary stars
Hubová, Dominika ; Pejcha, Ondřej (advisor) ; Kopáček, Ondřej (referee)
In this thesis we investigate the loss of mass from binary systems from the vicinity of the second Lagrange point L2. This phenomenon arises mainly in the common envelope evolutionary phase of close binary systems when the cores of the components orbit inside a shared gaseous envelope. It is a crucial but poorly understood stage in the system's development with two substantially different possible outcomes - stellar merger or formation of a close binary system with compact components. Modifying mass, energy and angular momentum of the binary, mass loss through the L2 point might significantly impact the system's evolution throughout the common envelope phase. Using numerical integration of equations of motion, we evaluate final states of test particles ejected from the proximity of the L2 point with arbitrary initial velocity with respect to the corotating reference frame. Furthermore, we compute the amount of energy and angular momentum these particles carry away from the system. Previously, only the particles ejected from the L2 point from initial corotation were studied; this work is therefore the first to address this problem with general initial conditions. Firstly, we initiate the particles at the L2 point with velocity pointing in the direction of x-axis and y-axis. Secondly, we eject the particles from...
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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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Chaotic motion in Johannsen-Psaltis spacetime
Zelenka, Ondřej ; Loukes Gerakopoulos, Georgios (advisor) ; Kopáček, Ondřej (referee)
The Johannsen-Psaltis spacetime is a perturbation of the Kerr spacetime de- signed to avoid pathologies like naked singularities and closed timelike curves. This spacetime depends not only on the mass and the spin of the central object, but also on extra parameters, making the spacetime deviate from Kerr; in this work we consider only the lowest order physically meaningful extra parameter. In this thesis we summarize the basics of the theory of regular and chaotic dynamics and we use numerical examples to show that geodesic motion in this spacetime can exhibit chaotic behavior. We study the corresponding phase space by using Poincaré sections and rotation numbers to show chaotic behavior both directly and indirectly (e.g. Birkhoff chains), and we use Lyapunov exponents to directly estimate the sensitivity to initial conditions for chaotic orbits. 1
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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...
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Transition from regular to chaotic motion in black hole magnetospheres
Kopáček, Ondřej ; Karas, Vladimír (advisor) ; Kulhánek, Petr (referee) ; Rezzolla, Luciano (referee)
Cosmic black holes can act as agents of particle acceleration. We study properties of a system consisting of a rotating black hole immersed in a large-scale organized magnetic field. Electrically charged particles in the immediate neighborhood of the horizon are influenced by strong gravity acting together with magnetic and induced electric components. We relax several constraints which were often imposed in previous works: the magnetic field does not have to share a common symmetry axis with the spin of the black hole but they can be inclined with respect to each other, thus violating the axial symmetry. Also, the black hole does not have to remain at rest but it can instead perform fast translational motion together with rotation. We demonstrate that the generalization brings new effects. Starting from uniform electro-vacuum fields in the curved spacetime, we find separatrices and identify magnetic neutral points forming in certain circumstances. We suggest that these structures can represent signatures of magnetic reconnection triggered by frame-dragging effects in the ergosphere. We further investigate the motion of charged particles in these black hole magnetospheres. We concentrate on the transition from the regular motion to chaos, and in this context we explore the characteristics of chaos in...
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