7 research outputs found
Pseudo-Schwarzschild Spherical Accretion as a Classical Black Hole Analogue
We demonstrate that a spherical accretion onto astrophysical black holes,
under the influence of Newtonian or various post-Newtonian pseudo-Schwarzschild
gravitational potentials, may constitute a concrete example of classical
analogue gravity naturally found in the Universe. We analytically calculate the
corresponding analogue Hawking temperature as a function of the minimum number
of physical parameters governing the accretion flow. We study both the
polytropic and the isothermal accretion. We show that unlike in a general
relativistic spherical accretion, analogue white hole solutions can never be
obtained in such post-Newtonian systems. We also show that an isothermal
spherical accretion is a remarkably simple example in which the only one
information--the temperature of the fluid, is sufficient to completely describe
an analogue gravity system. For both types of accretion, the analogue Hawking
temperature may become higher than the usual Hawking temperature. However, the
analogue Hawking temperature for accreting astrophysical black holes is
considerably lower compared with the temperature of the accreting fluid.Comment: Final Version to appear in the journal General Relativity &
Gravitation, Volume 27, Issue 11, 2005. 17 pages, Two colour and one black
and white figures. Typos corrected. Recent reference on analogue effect in
relativistic accretion disc adde
An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion
We apply the theory of algebraic polynomials to analytically study the
transonic properties of general relativistic hydrodynamic axisymmetric
accretion onto non-rotating astrophysical black holes. For such accretion
phenomena, the conserved specific energy of the flow, which turns out to be one
of the two first integrals of motion in the system studied, can be expressed as
a 8 degree polynomial of the critical point of the flow configuration.
We then construct the corresponding Sturm's chain algorithm to calculate the
number of real roots lying within the astrophysically relevant domain of
. This allows, for the first time in literature, to {\it
analytically} find out the maximum number of physically acceptable solution an
accretion flow with certain geometric configuration, space-time metric, and
equation of state can have, and thus to investigate its multi-critical
properties {\it completely analytically}, for accretion flow in which the
location of the critical points can not be computed without taking recourse to
the numerical scheme. This work can further be generalized to analytically
calculate the maximal number of equilibrium points certain autonomous dynamical
system can have in general. We also demonstrate how the transition from a
mono-critical to multi-critical (or vice versa) flow configuration can be
realized through the saddle-centre bifurcation phenomena using certain
techniques of the catastrophe theory.Comment: 19 pages, 2 eps figures, to appear in "General Relativity and
Gravitation
The procedure of evaluation of the resource potential of the enterprise
Теоретичне обґрунтування і практична розробка інструментів структурного відтворення ресурсного потенціалу. Вивчено та проаналізовано методи оцінки ефективності використання ресурсного потенціалу підприємства. Розглянуто оціночні показники і параметри якісної оцінки складових ресурсного потенціалу підприємства. Запропоновано модель причинно-наслідкового взаємозв'язку ресурсного потенціалу, конкурентоспроможності та стратегічного розвитку підприємства. Наведена методика розрахунку середньозваженого показника оцінки ефективності використання ресурсного потенціалу підприємства.Теоретическое обоснование и практическая разработка инструментов структурного воспроизводства ресурсного потенциала. Изучены и проанализированы методы оценки эффективности использования ресурсного потенциала предприятия. Рассмотрены оценочные показатели и параметры качественной оценки составляющих ресурсного потенциала предприятия. Предложена модель причинно-следственной взаимосвязи ресурсного потенциала, конкурентоспособности и стратегического развития предприятия. Представленная методика расчета средневзвешенного показателя оценки эффективности использования ресурсного потенциала предприятия.Theoretical substantiation and practical development of tools for structural reproduction of resource potential. Researched and analyzed methods of evaluating the effectiveness of using resource potential at enterprises. Considers performance indicators and parameters for quality evaluation of components of resource potential of the enterprise. The proposed model of causal relationships resource potential, competitiveness and strategic development of the enterprise. The technique of calculating the weighted average of the efficiency evaluation of the resource potential of the enterprise