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Thermodynamics of spacetime: A new perspective from the quantum realm
Liška, Marek ; Alonso Serrano, Ana (advisor) ; Oriti, Daniele (referee)
The main result of the thesis is the derivation of quantum phenomenological gravi- tational dynamics from the thermodynamics of local causal diamonds. By taking into account logarithmic corrections to entropy implied by quantum gravity effects, we derive new gravitational equations of motion which incorporate quantum corrections. The re- sulting theory appears to be a direct generalisation of the classical unimodular gravity instead of the general relativity. Upon obtaining the equations, we discuss their prop- erties and possible implications. As by-products, we also present a novel derivation of the Einstein equations from the thermodynamics of causal diamonds and a derivation of the logarithmic corrections to black hole entropy from the existence of minimal re- solvable area. Apart from the new results, we also provide an extensive review of the thermodynamics of local causal horizons. 1
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Exact spacetimes and their physical properties
Veselý, Jiří ; Žofka, Martin (advisor) ; Hennigar, Robie (referee) ; Tahamtan, Tayebeh (referee)
Motivated by our desire to find generalizations of the Bonnor-Melvin spacetime, the thesis investigates seven static, cylindrically-symmetric and electrovacuum exact solutions to the Einstein-Maxwell equations. They contain a magnetic field and six of them also include the cosmological constant. After discussing some of the methods we use during our investigation, we present the basic properties of the spacetimes, and for each of them we also study charged test particle motion and their admissible shell sources composed of particle streams. We also perform numerical computations to determine whether the equations admit more general solutions than the exact ones we derived. 1
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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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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.
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Chaotic Motion around Black Holes
Suková, Petra ; Semerák, Oldřich (advisor) ; Šubr, Ladislav (referee) ; Loukes-Gerakopoulos, Georgios (referee)
As a non-linear theory of space-time, general relativity deals with interesting dynamical systems which can be expected more prone to chaos than their Newtonian counter-parts. In this thesis, we study the dynamics of time- like geodesics in the static and axisymmetric field of a Schwarzschild black hole surrounded, in a concentric way, by a massive thin disc or ring. We reveal the rise (and/or decline) of geodesic chaos in dependence on parameters of the sys- tem (the disc/ring mass and position and the test-particle energy and angular momentum), (i) on Poincaré sections, (ii) on time series of position and their power spectra, (iii) by applying two simple yet powerful recurrence methods, and (iv) by computing Lyapunov exponents and two other related quantifiers of or- bital divergence. We mainly focus on "sticky" orbits whose different parts show different degrees of chaoticity and which offer the best possibility to test and compare different methods. We also add a treatment of classical but dissipative system, namely the evolution of a class of mechanical oscillators described by non-standard constitutive relations.
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Solving test-particle equations of motion near a black hole
Ryston, Matěj ; Ledvinka, Tomáš (advisor) ; Suková, Petra (referee)
Bachelor thesis Matěj Ryston 2011/2012 Abstract in English This work aims to give a well-arranged summary of the description and solving the equations of motion of particles outside a black hole (a star) with emphasis on numerical solutions. For that purpose a summary of numerical methods for solving ordinary differential equations, together with a review and comparison of chosen methods, is given. In the second chapter follows a brief recall of the foundations of General Relativity as well as the description of the geometry of Schwarzschild solution of the Einstein equations. After that equations of motion are formulated. In conclusion, selected numerical methods are used on solving said equations of motion of a test particle or those describing bending of light rays in closeness to a black hole.
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Modeling the Mach's principle in the post-Minkowskian approximation to general relativity
Schmidt, Tibor ; Ledvinka, Tomáš (advisor) ; Kofroň, David (referee)
The aim of this thesis is the simulation of relativistic phenomena in post- Minkowskian approximation. In the introduction the terms of Mach principle and gravitomagnetism are presented. Afterwards the principles of numeric solution of ordinary differential equations are summarized. Consequently, we get acquainted with the first post-Minkowskian approximation in canonical formalism and with elementary examples of its use. In the next chapter the results of performed simulations of classical General Relativity tests are described. The last chapter is devoted to the simulation of gravitomagnetism and of the system of rotating particles.
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Termodynamika černých děr. Entropie a informace.
Liška, Marek ; Acquaviva, Giovanni (advisor) ; Scholtz, Martin (referee)
The aim of the thesis is to provide a review of black hole thermodynamics and its relation with concepts of entropy and physical information. We start by deriving the four laws of black hole thermodynamics in the context of classical general relativity. To supplement this, we use semiclassical limit of quantum mechanics to show that black holes radiate and have non-zero thermodynamic temperature. In the second part of the thesis we describe the concepts of the Shannon and von Neumann entropy and of physical information. Lastly, we discuss the use of these concepts in the context of black hole mechanics. 1
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Superluminal motion in general relativity
Gattermann, Rico ; Ledvinka, Tomáš (advisor) ; Krtouš, Pavel (referee)
We show how superluminal travel can be achieved by means of the Alcubierre warp drive. In this spacetime a spaceship locally at rest is surrounded by a "bubble" moving faster than the speed of light. We derive the equations of motion for photons and massive particles and illustrate properties of their solutions. We will find that warp drives cause frequency shifts and refraction of light passing the bubble wall, which affects the view of the outside universe seen by a traveller on spaceship. As for superluminal warp drives, existence of horizons will be shown. We will discuss that the stress-energy tensor, generating a warp corridor in spacetime, is not related to any classical field or matter, and attempts to interpret it via quantum mechanics resulted in extreme amounts of matter required. Powered by TCPDF (www.tcpdf.org)
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Superluminal motion in general relativity
Gattermann, Rico ; Ledvinka, Tomáš (advisor) ; Krtouš, Pavel (referee)
We show how superluminal travel can be achieved by means of the Alcubierre warp drive. In this spacetime a spaceship locally at rest is surrounded by a "bubble" moving faster than the speed of light. We derive the equations of motion for photons and massive particles and illustrate properties of their solutions. We will find that warp drives cause frequency shifts and refraction of light passing the bubble wall, which affects the view of the outside universe seen by a traveller on spaceship. As for superluminal warp drives, existence of horizons will be shown. We will discuss that the stress-energy tensor, generating a warp corridor in spacetime, is not related to any classical field or matter, and attempts to interpret it via quantum mechanics resulted in extreme amounts of matter required. Powered by TCPDF (www.tcpdf.org)
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