A method to determine the parameters of black holes in AGNs and galactic X-ray sources with periodic modulation of variability

We propose a simple and unambiguous way to deduce the parameters of black holes which may reside in AGNs and some types of X-ray binaries. The black-hole mass and angular momentum are determined in physical units. The method is applicable to the sources with periodic components of variability, provided one can assume the following: (i) Variability is due to a star or a stellar-mass compact object orbiting the central black hole and passing periodically through an equatorial accretion disk (variability time-scale is given by the orbital period). (ii) The star orbits almost freely, deviation of its trajectory due to passages through the disk being very weak (secular); the effect of the star on the disk, on the other hand, is strong enough to yield observable photometric and spectroscopic features. (iii) The gravitational field within the nucleus is that of the (Kerr) black hole, the star and the disk contribute negligibly.Comment: 17 pages, 4 figures, 2 tables; LaTeX2.09 (aas2pp4.sty); submitted to the Astrophysical Journal; also available at http://astro.mff.cuni.cz/karas/papers.htm with additional illustration

Description of Pseudo-Newtonian Potential for the Relativistic Accretion Disk around Kerr Black Holes

We present a pseudo-Newtonian potential for accretion disk modeling around the rotating black holes. This potential can describe the general relativistic effects on accretion disk. As the inclusion of rotation in a proper way is very important at an inner edge of disk the potential is derived from the Kerr metric. This potential can reproduce all the essential properties of general relativity within 10% error even for rapidly rotating black holes.Comment: 5 Latex pages including 1 figure. Version to appear in Astrophysical Journal, V-581, N-1, December 10, 200

On the gravitomagnetic effects in cylindrically symmetric spacetimes

Using gyroscopes we generalize results, obtained for the gravitomagnetic clock effect in the particular case when the exterior spacetime is produced by a rotating dust cylinder, to the case when the vacuum spacetime is described by the general cylindrically symmetric Lewis spacetime. Results are contrasted with those obtained for the Kerr spacetime.Comment: 11 pages Latex, to appear in J.Math.Phy

Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes

We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-reversal of these in the case of stationary spacetimes is discussed. Further insight is gained in the case of static spacetime by considering the phenomena in a spacetime conformal to the original one. Gravi-electric and gravi-magnetic fields are studied and their relation to inertial forces is established.Comment: 21 pages, latex, no figures, http://202.41.67.76/~nayak/gpifass.te

Generalized pseudo-Newtonian potential for studying accretion disk dynamics in off-equatorial planes around rotating black holes: Description of a vector potential

We prescribe a pseudo-Newtonian vector potential for studying accretion disks around Kerr black holes. The potential is useful to study the inner properties of disk not confined to the equatorial plane where general relativistic effect is indispensable. Therefore, we incorporate the essential properties of the metric at the inner radii through the pseudo-Newtonian potential derived from the general Kerr spacetime. The potential, reproducing most of the salient features of the general-relativity, is valid for entire regime of Kerr parameter. It reproduces the last stable circular orbit exactly as that in the Kerr geometry. It also reproduces last bound orbit and energy at last stable circular orbit with a maximum error ~7% and ~15% respectively upto an orbital inclination 30 degree.Comment: 22 AASTeX pages including 5 postscript figures; Accepted for publication in The Astrophysical Journa

Розроблення методу розрахунку процесу газифікації низькосортного палива у суцільному шарі на основі експериментальних досліджень

The composition and calorific value of the synthesis gas obtained as a result of gasification of low-grade fuel may vary depending on various factors. The main factors influencing the process of wood gasification are the size of the particles, the amount of air supplied to the gasification chamber, and a number of other factors depending on the gas that is gasified and the parameters of the gasifier. To date, the physical models of the solid fuel gasification process have been developed and covered in literary sources and scientific articles, which allow to construct a method for calculating the parameters of the working process in a gasifier based on the equations of thermal and material balances, the burning and carbonization of gas, and also heat exchange of particles with a layer and with the wall of the gas generator. However, these physical models are designed for a specific type of gasifier. Therefore, there is a need to develop a method for calculating the wood gasification process, which will allow calculation of the parameters of the working process in a gasifier with a continuous layer, which is most technologically and constructively simple. The main goal of the work is to develop a method for calculating the gasification process of low-grade fuel, which will allow the calculation of the parameters of the working process in a gasifier with a continuous layer, which is the most technologically and structurally simple. Used standardized methods for conducting research of the process of gasification of low-grade fuel. In the process of developing a gas generator plant, which allows the production of synthesis gas, modern methods of using appropriate monitoring devices are used. Used mathematical planning of experimental research. A method has been developed for calculating the process of wood gasification, which allows the calculation of the parameters of the working process in a gasifier with a continuous layer, based on the equations of heat and material balances. Based on experimental studies, the material and heat balance of the pine gasification gasification process (Pinus sylvestris) was compiled. It is shown that during gasification of pine wood, small heat losses are obtained as a result of dust removal and carbon losses with ash and slag.Розроблено метод розрахунку процесу газифікації низькосортного палива, який дає змогу провести розрахунок параметрів робочого процесу в газифікаторі зі суцільним шаром, який є найбільш технологічно та конструктивно простим. Проаналізовано фізичні моделі процесу газифікації твердого палива, які дають змогу побудувати методику розрахунку параметрів робочого процесу у газифікаторі, засновану на рівняннях теплового і матеріального балансів, вигорання і газифікації вуглецю, що сприяє підвищенню екологічних показників та модернізації наявних інженерних методів розрахунку. Використано стандартизовані методи проведення досліджень процесу газифікації низькосортного палива. У процесі розроблення газогенераторної установки, що дає змогу виробляти синтез-газ, застосовано сучасні методи використання відповідних контрольно-вимірювальних пристроїв. Використано математичне планування експериментальних досліджень. Розроблено метод розрахунку процесу газифікації деревини, який дає змогу провести розрахунок параметрів робочого процесу в газифікаторі зі суцільним шаром, засновану на рівняннях теплового і матеріального балансів. На основі експериментальних досліджень складено матеріальний і тепловий баланси процесу газифікації деревини породи сосна (Pinus sylvestris). Показано, що під час газифікації соснової деревини невеликі втрати тепла виходять внаслідок винесення пилу і втрат вуглецю із золою і шлаком