We consider a novel extension of the recently proposed mimetic gravity. The latter is a scalar-tensor theory which is able to describe dark matter on cosmological scales. Moreover, this theory can be considered as a low energy limit of the projectable Horava-Lifshitz gravity. The proposed novel extension directly couples gradients of the mimetic scalar field to the curvature tensor. These couplings introduce into the energy momentum tensor an anisotropic stress which is non-vanishing even at the first order in perturbations around a cosmological background. Further we show that such terms modify the formula for the speed of sound of scalar perturbations and even more importantly change the speed of propagation for the gravitational waves. The appearance of the anisotropic stress and the consequent nontrivial speed of propagation of the gravity waves are new phenomena which were not present in the previously studied mimetic models. Furthermore, we demonstrate that the effective Newton's gravitational constant in the background Friedmann equations is shifted in the presence of the novel couplings of the mimetic scalar field. We calculate the quadratic action for scalar and tensor perturbations and briefly discuss possible instabilities. Finally we consider the current observational bounds on the model....

Regional integration such as ECOWAS is believed to be an important element to stimulate trade, which could lead to economic growth and development for countries in this regional group. Despite the efforts made at creating this regional group in West Africa, the benefits from intra regional trade have been unsatisfactory. The study examined the role of Nigeria in the integration processes in Africa and to quantify the impact of this regional group on trade and economic performance in Nigeria. Cross sectional time series data for 17 years from 1996 to 2012 were analysed using an augmented (or extended) gravity equation. Results show that being in ECOWAS has contributed very little to trade and economic performance in Nigeria. Lack of political will to implement treaty provisions, poor infrastructure, non diversification of individual countries' economies among other have been identified as the problem causing the very low level of intra regional trade in ECOWAS. There are potential gains to be made in ECOWAS including Nigeria if significant effort are made to implement policy recommendations

Temnáenergietvořícípřibližně70%hmotyvesmíruz·stávájednouznejvětšch záhad moderní fyziky. K pochopení její podstaty jsou potřeba přesná kosmolog- ická měření. Jedním z projekt· zkoumající tuto exotickou formu hmoty bude i Large Synoptic Survey Telescope, který pom·že potvrdit či vyvrátit standardní kosmologický model (ΛCDM). Pro úspěch projektu je potřeba prozkoumat r·zné teorie temné energie. Jednou z alternativních teoríí vysvětlujících urychlenou expanzi vesmíru je tzv. chameleoní gravitace. Chameleon je nové skalární pole s hmotou závisející na okolní hustotě. V hustých prostředích jako je například Sluneční soustava získává pole velkou hmotu a propaguje se pouze na malých vzdálenostech díky čemuž m·že uniknout standardním test·m gravitace. V prá- ci mimo jiné studujeme chování chameleoního pole v okolí hvězd a v galaxiích. Ukazujeme také za jakých okolností je toto pole možné detekovat pomocí spek- troskopických měření a slabého čočkování.

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

vii Title: General relativity in higher dimensions Author: Tomáš Málek Institute: Institute of Theoretical Physics Supervisor: Mgr. Vojtěch Pravda, PhD., Institute of Mathematics of the Academy of Sciences of the Czech Republic Abstract: In the first part of this thesis, Kerr-Schild metrics and extended Kerr- Schild metrics are analyzed in the context of higher dimensional general relativ- ity. Employing the higher dimensional generalizations of the Newman-Penrose formalism and the algebraic classification of spacetimes based on the existence and multiplicity of Weyl aligned null directions, we establish various geometri- cal properties of the Kerr-Schild congruences, determine compatible Weyl types and in the expanding case discuss the presence of curvature singularities. We also present known exact solutions admitting these Kerr-Schild forms and con- struct some new ones using the Brinkmann warp product. In the second part, the influence of quantum corrections consisting of quadratic curvature invariants on the Einstein-Hilbert action is considered and exact vacuum solutions of these quadratic gravities are studied in arbitrary dimension. We investigate classes of Einstein spacetimes and spacetimes with a null radiation term in the Ricci tensor satisfying the vacuum field equations of quadratic gravity...

This thesis pursues the topic of downtrends in Czech intonation in correlation with the geographical origin of speakers. The theoretical part is devoted to the section on the suprasegmental plateaux of the language - the intonation, the intonation variability, and mainly the intonation downtrends. It also brings a selective dialectical description of three Czech regions, which this thesis deals with: Plzeňsko, Štítecko and Břeclavsko. The practical part is targeted to the intonational analysis of the speech material (74 speakers overall), acquired in the previously mentioned regions. The average caliber of the guidelines, acquired by the application of the regressive line, were − for the given groups of speakers − compared and annotated, considering the age and sex of the respondents, (ideal) number of tacts or relative presence of the finding questions. key words: intonation, intonational downtrends, region, speaker, regressive line

Title: Model Problems of the Theory of Gravitation Author: Marián Pilc Department: Institute of Theoretical Physics Faculty of Mathematics and Physics Supervisor: prof. RNDr. Jiří Bičák, DrSc., dr. h. c., Institute of Theoretical Physics Faculty of Mathematics and Physics Abstract: Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action of the Einstein-Cartan theory are derived. Ad- ditional gauge freedom is geometrically interpreted. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over spatial sec- tion. The second class constraints are analyzed and Dirac bracket is defined.Reduction of phase space is performed and canonical coordinates are introduced. The second part of this thesis is dedicated to quantum formulation of Einstein-Cartan theory. Point version of Einstein-Cartan phase space is introduced. Basic variables, crucial for quan- tization, are derived via groups acting on the phase space and their selfadjoint represen- tation is found. Representation of basic variables of Einstein-Cartan theory is derived via infinite...

Probabilistic Spacetime is a simple generalization of the classical model of spa- cetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a generalization is a possible application in the context of some quantum gravity approaches, na- mely those using the path integral. It is argued that this model might be used to restrict the precision of the geometry on small scales without postulating discrete structure; or it may be used as an effective description of a probabilistic geometry resulting from a full-fledged quantum gravity computation.

Title: Selected gravitational effects in the Universe Author: Mgr. Tomáš Franc Department: Astronomical Institute of Charles University Supervisor: doc. RNDr. Marek Wolf, CSc., Astronomical Institute of Charles University Abstract: In this Thesis we have given an overview of tidal phenomena with their explanations and also explained the gravitational assist with examples of its use. We have created many pictures and 17 animations for better understanding of these topics. This part of the Thesis is focused on high school students and their teachers, it can be used by teachers for their inspiration for lessons, or students and more generally people interested in these topics can read this part as a study text. The main part of the Thesis is the result of research conducted on 13 high schools in the Czech Republic. 800 students took part in the research; its purpose was to find out students' knowledge of tidal phenomena and the gravitational assist. The research was carried out in the form of questionnaires. Keywords: gravity, tidal phenomena, gravitational assist, pedagogical research

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...