1. INFLUENCE OF COSMOLOGICAL CONSTANT ON PARTICLE DYNAMICS NEAR COMPACT OBJECTS Zdeněk Stuchlík, Petr Slaný, Jiří Kovář and Stanislav Hledík Institute of Physics Silesian University in Opava Czech Republic João Pessoa, July, 2008 This work was supported by the Czech grant MSM 4781305903 7th ALEXANDER FRIEDMANN INTERNATIONAL SEMINAR ON GRAVITATION AND COSMOLOGY

2. Introduction 1) test particle motion 2) spinning test particle motion 3) perfect fluid equilibrium configuration Schwarzschild-de Sitter geometry Kerr-de Sitter geometry A) standard general relativistic approach B) inertial forces approach C) pseudo-Newtonian approach

3. Kerr-de Sitter geometry Metric line element metric coefficients dimensionless cosmological parameter

4. Kerr-de Sitter geometry Equatorial plane

5. Kerr-de Sitter geometry Embedding diagrams Schwarzschild Schwarzschild-de Sitter

6. Carter’s equations effective potential Test particle motion Standard relativistic approach [Stuchlik and Hledik, Physical Review D (60), 1999] [Stuchlik and Slany, Physical Review D (69), 2004]

7. Test particle motion Effective potential Schwarzschild-de Sitter Kerr-de Sitter

8. Test particle motion Schwarzschild-de Sitter horizons marginally bound marginally stable

9. special observers geodetical motion inertial forces Test particle motion Inertial force formalism [Kovar and Stuchlik, Int. Journal of Modern Phys. A (21), 2006] [Kovar and Stuchlik, Class. Quantum Grav. (24), 2007]

10. Test particle motion Forces behaviour Kerr-de SitterKerr Schwarzschild Schwarzschild-de Sitter

11. Test particle motion Basic features ergosphere static radius

12. Test particle motion Kerr-de Sitter

13. Test particle motion Schwarzschild-de Sitter

14. Test spinning particle motion [Stuchlik, Acta Phys. Slovaca (49),1999] [Stuchlik and Kovar, Class. Quantum Grav. (23), 2006]

15. Test spinning particle motion

16. Perfect fluid equilibrium configurations [Stuchlik, Slany and Hledik, Astronomy and Astrophysics (363), 2000] [Slany and Stuchlik, Class. Quantum Grav. (22), 2005]

17. Perfect fluid equilibrium configurations W=const. contours W-behaviour (equatorial plane)

18. Pseudo-Newtonian approach Schwarzschild-de Sitter pseudo-Newtonian potential approximative approach Newtonian routines + relativistic effects (cosmological repulsion) [Stuchlik and Kovar, Int. Journal of Modern Physics D (in print), 2008] (eprint (gr-qc) arXiv:0803.3641)

19. exact determination of - horizons - static radius - marginally stable circular orbits - marginally bound circular orbits - cusps of tori - critical equipressure surfaces small differences when determining - effective potential (energy) barriers mass of the toroidal structures matter outflow Pseudo-Newtonian approach Schwarzschild-de Sitter

20. Thank you