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$^{th}$ 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 $\mathbb{R}$. 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