Forces in Kerr spacetimes with a repulsive cosmological constant

Forces defined in the framework of optical reference geometry are introduced in the case of stationary and axially symmetric Kerr black-hole and naked-singularity spacetimes with a repulsive cosmological constant. Properties of the forces acting on test particles moving along circular orbits in the equatorial plane are discussed, whereas it is shown where the gravitational force vanishes and changes its orientation and where the centrifugal force vanishes and changes its orientation independently of the velocity of test particles related to the optical geometry; the Coriolis force does not vanish for the velocity being non-zero. The spacetimes are classified according to the number of circular orbits where the gravitational and centrifugal forces vanish

The proposal of flood protection measure in the village Lichnov.

Import 02/11/2016Diplomová práce se zabývá návrhem protipovodňového opatření v obci Lichnov. Projekt je rozdělen na část teoretickou a část praktickou. Teoretická část popisuje stávající stav daného území, hydrologické a klimatické poměry. Následuje identifikace problému v místě, kterým se projekt zabývá dále legislativní a technické řešení problému. Teoretická část se zabývá také tématu povodní jako takových. V praktické části se zabývám samotnými variantami řešení a jejich následnému rozpracováni. Vybraný návrh se zabývá návrhem tělesa hráze, výpustného zařízení, bezpečnostního přelivu a je dále podložen textovou částí, hydrotechnickými výpočty a výkresovou dokumentací.This thesis describes the design of flood protection measures in the village Lichnov. The project is divided into theoretical and practical part. The theoretical part describes the current state of the territory, hydrological and climatic conditions. Following identification of the problem at the point addressed by the project further legislative and technical problem solving. The theoretical part also deals with the topic of flooding as such. In the practical part I write about various solutions and their subsequent elaboration. The successful proposal describes the design of the dam, discharge facilities, emergency spillway and is further supported by the text part, hydro-technical calculations and drawings.Prezenční546 - Institut environmentálního inženýrstvívelmi dobř

Pseudo-Newtonian gravitational potential for Schwarzschild-de Sitter spacetimes

Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test-particle motion is constructed and compared with its general relativistic counterpart given by the Schwarzschild-de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion discs in astrophysically interesting situations in large galactic structures for the Schwarzschild-de Sitter spacetimes with the cosmological parameter y=(1/3)\Lambda M^2<10^{-6}.Comment: 17 pages, 11 figures, accepted by International Journal of Modern Physics D (2008

Equilibrium conditions of spinning test particles in Kerr-de Sitter spacetimes

Equilibrium conditions and spin dynamics of spinning test particles are discussed in the stationary and axially symmetric Kerr-de Sitter black-hole or naked-singularity spacetimes. The general equilibrium conditions are established, but due to their great complexity, the detailed discussion of the equilibrium conditions and spin dynamics is presented only in the simple and most relevant cases of equilibrium positions in the equatorial plane and on the symmetry axis of the spacetimes. It is shown that due to the combined effect of the rotation of the source and the cosmic repulsion the equilibrium is spin dependent in contrast to the spherically symmetric spacetimes. In the equatorial plane, it is possible at the so-called static radius, where the gravitational attraction is balanced by the cosmic repulsion, for the spinless particles as well as for spinning particles with arbitrarily large azimuthal-oriented spin or at any radius outside the ergosphere with a specifically given spin orthogonal to the equatorial plane. On the symmetry axis, the equilibrium is possible at any radius in the stationary region and is given by an appropriately tuned spin directed along the axis. At the static radii on the axis the spin of particles in equilibrium must vanish

Role of electric charge in shaping equilibrium configurations of fluid tori encircling black holes

Astrophysical fluids may acquire non-zero electrical charge because of strong irradiation or charge separation in a magnetic field. In this case, electromagnetic and gravitational forces may act together and produce new equilibrium configurations, which are different from the uncharged ones. Following our previous studies of charged test particles and uncharged perfect fluid tori encircling compact objects, we introduce here a simple test model of a charged perfect fluid torus in strong gravitational and electromagnetic fields. In contrast to ideal magnetohydrodynamic models, we consider here the opposite limit of negligible conductivity, where the charges are tied completely to the moving matter. This is an extreme limiting case which can provide a useful reference against which to compare subsequent more complicated astrophysically-motivated calculations. To clearly demonstrate the features of our model, we construct three-dimensional axisymmetric charged toroidal configurations around Reissner-Nordstr\"om black holes and compare them with equivalent configurations of electrically neutral tori.Comment: 14 pages, 7 figure

Constraining models of twin peak quasi-periodic oscillations with realistic neutron star equations of state

Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. In our previous work we have considered several QPO models. We have identified and explored mass-angular-momentum relations implied by individual QPO models for the atoll source 4U 1636-53. In this paper we extend our study and confront QPO models with various NS equations of state (EoS). We start with simplified calculations assuming Kerr background geometry and then present results of detailed calculations considering the influence of NS quadrupole moment (related to rotationally induced NS oblateness) assuming Hartle-Thorne spacetimes. We show that the application of concrete EoS together with a particular QPO model yields a specific mass-angular-momentum relation. However, we demonstrate that the degeneracy in mass and angular momentum can be removed when the NS spin frequency inferred from the X-ray burst observations is considered. We inspect a large set of EoS and discuss their compatibility with the considered QPO models. We conclude that when the NS spin frequency in 4U 1636-53 is close to 580Hz we can exclude 51 from 90 of the considered combinations of EoS and QPO models. We also discuss additional restrictions that may exclude even more combinations. Namely, there are 13 EOS compatible with the observed twin peak QPOs and the relativistic precession model. However, when considering the low frequency QPOs and Lense-Thirring precession, only 5 EOS are compatible with the model.Comment: 12 pages, 9 figures, 3 tables, accepted for publication in The Astrophysical Journa

Mass of the active galactic nucleus black hole XMMUJ134736.6+173403

A recent study of the X-ray source XMMUJ134736.6+173403 has revealed a strong quasi-periodic modulation of the X-ray flux. The observation of two quasiperiodic oscillations (QPOs) that occur on a daily timescale and exhibit a 3:1 frequency ratio strongly supports the evidence for the presence of an active galactic nucleus black hole (AGN BH). Assuming the orbital origin of QPOs we calculate the upper and lower limit on AGN BH mass M arriving at $M\approx 10^7-10^9M_{\odot}$. Comparing that to mass estimates of other sources, MMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on AGN BH mass based on QPO observations. We note it will be crucial for the falsification of particular resonance models of QPOs whether only single QPO with frequency that completes the harmonic sequence 3:2:1 is found in this source, or whether there is a new different pair of QPOs with frequencies in the 3:2 ratio. The former case would agree with the prediction of the 3:2 epicyclic resonance model and black hole mass $M\approx(5a^2 + 8a + 8)\times 10^{7}M_{\odot}$, where a is a dimensionless BH spin.Comment: 5 pages, 2 figures, 1 table, accepted for publication in A&A Letters, minor corrections to the text to match published versio