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

МОДЕЛЮВАННЯ ТЕРМОГАЗОДИНАМІЧНИХ ПАРАМЕТРІВ СТРУМЕНЯ ВОДНЮ У РАЗІ РОЗГЕРМЕТИЗАЦІЇ КОРПУСА ТУРБОГЕНЕРАТОРА ЕЛЕКТРИЧНОЇ СТАНЦІЇ

Theoretical research of parameters of free stream of hydrogen, which flows out of the damaged body of turbogenerator in the apartment of machine hall is conducted. The received correlations allow to determine the thermodynamics parameters of hydrogen stream (speed of profluim, temperature of hydrogen stream on exit from the emergency opening in the body of turbogenerator, duration of profluvium during change of area of the emergency opening and pressure overfall) in the case of emergency situation (damage of gas and oil compression system).Проведено теоретичні дослідження параметрів вільного струменя водню, який витікає з пошкодженого корпусу турбогенератора в приміщення машинного залу. Отримані співвідношення дають змогу визначати термодинамічні параметри струменя водню (швидкість витікання, температуру струменя водню на виході з аварійного отвору в корпусі турбогенератора, тривалість витікання при зміні площі аварійного отвору і перепаду тиску) у разі виникнення аварійної ситуації (пошкодження системи газооливного ущільнення)

Narrow Components within the Fe Kalpha Profile of NGC 3516: Evidence for the Importance of General Relativistic Effects?

We present results from a simultaneous Chandra HETG and XMM-Newton observation of NGC 3516. We find evidence for several narrow components of Fe Kalpha along with a broad line. We consider the possibility that the lines arise in an blob of material ejected from the nucleus with velocity ~0.25c. We also consider an origin in a neutral accretion disk, suffering enhanced illumination at 35 and 175 gravitational radii, perhaps due to magnetic reconnection. The presence of these narrow features indicates there is no Comptonizing region along the line-of-sight to the nucleus. This in turn is compelling support for the hypothesis that broad Fe Kalpha components are, in general, produced by strong gravity.Comment: 12 pages, 3 color figures. LaTeX with postscript figures. Resubmitted June 7 2002, to Astrophysical Journal Letter

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ТА ДОСЛІДЖЕННЯ ВЕЛИЧИНИ ТЕПЛОВОГО ПОТОКУ ФАКЕЛА ПОЖЕЖІ

The method of determining heat flow coming from fire to fire equipment, depending on the temperature of the flame, its size, distance to the centre of the fire is suggested. On the basis of laws of heat radiation the dependence of the heat flux flame on its temperature, size, distance to nearby objects, position in space is investigated. The results are depicted graphically.Запропоновано методику визначення теплових потоків, спрямованих від пожежі до пожежної техніки залежно від температури полум’я, його розмірів, віддалі до осередку пожежі. На основі законів теплообміну випромінюванням досліджено залежність величини теплового потоку полум’я від його температури, розмірів, віддалі до найближчих предметів, розташування в просторі. Результати досліджень зображені графічно

An extended scheme for fitting X-ray data with accretion disk spectra in the strong gravity regime

Accreting black holes are believed to emit X-rays which then mediate information about strong gravity in the vicinity of the emission region. We report on a set of new routines for the Xspec package for analysing X-ray spectra of black-hole accretion disks. The new computational tool significantly extends the capabilities of the currently available fitting procedures that include the effects of strong gravity, and allows one to systematically explore the constraints on more model parameters than previously possible (for example black-hole angular momentum). Moreover, axial symmetry of the disk intrinsic emissivity is not assumed, although it can be imposed to speed up the computations. The new routines can be used also as a stand-alone and flexible code with the capability of handling time-resolved spectra in the regime of strong gravity. We have used the new code to analyse the mean X-ray spectrum from the long XMM--Newton 2001 campaign of the Seyfert 1 galaxy MCG--6-30-15. Consistent with previous findings, we obtained a good fit to the broad Fe K line profile for a radial line intrinsic emissivity law in the disk which is not a simple power law, and for near maximal value of black hole angular momentum. However, equally good fits can be obtained also for small values of the black hole angular momentum. The code has been developed with the aim of allowing precise modelling of relativistic effects. Although we find that current data cannot constrain the parameters of black-hole/accretion disk system well, the approach allows, for a given source or situation, detailed investigations of what features of the data future studies should be focused on in order to achieve the goal of uniquely isolating the parameters of such systems.Comment: Accepted for publication in ApJ S

ВИБІР ТА ОБҐРУНТУВАННЯ КОНСТРУКТИВНОЇ СХЕМИ АВТОМАТИЧНОГО РЕГУЛЯТОРА ШВИДКОСТІ ІНДИВІДУАЛЬНОГО ПОЖЕЖНО-РЯТУВАЛЬНОГО ПРИСТРОЮ

The method of people evacuation during fires in high- rise buildings with the use of devices with the automatic adjusting of load lowering speed is considered. Different structural chans of individual rescuing facilities are presented, their advantages and disadvantages are analyzed, perspective directions of constructing of such devices are specified.Розглядається один із можливих способів евакуації людей при пожежах в висотних будівлях з використанням пристроїв з автоматичним регулюванням швидкості опускання вантажу. Приводяться різні конструктивні схеми індивідуальних рятувальних засобів, аналізуються їх переваги та недоліки, вказуються перспективні напрями конструювання таких пристроїв