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 th ALEXANDER FRIEDMANN INTERNATIONAL SEMINAR ON GRAVITATION AND COSMOLOGY

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

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

Kerr-de Sitter geometry Equatorial plane

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

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]

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

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

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]

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

Test particle motion Basic features ergosphere static radius

Test particle motion Kerr-de Sitter

Test particle motion Schwarzschild-de Sitter

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

Test spinning particle motion

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

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

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: )

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

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