influence of cosmological constant on particle dynamics near compact objects zdeněk stuchlík, petr...
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INFLUENCE OF COSMOLOGICAL CONSTANTON PARTICLE DYNAMICS NEAR COMPACT OBJECTS
Zdeněk Stuchlík, Petr Slaný, Jiří Kovář and Stanislav Hledík
Institute of PhysicsSilesian 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
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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
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Kerr-de Sitter geometry Metric
• line element
• metric coefficients
• dimensionless cosmological parameter
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Kerr-de Sitter geometry Equatorial plane
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Kerr-de Sitter geometry Embedding diagrams
Schwarzschild Schwarzschild-de Sitter
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• 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]
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Test particle motion Effective potential
Schwarzschild-de Sitter Kerr-de Sitter
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Test particle motion Schwarzschild-de Sitter
horizons
marginally bound
marginally stable
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• 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]
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Test particle motion Forces behaviour
Kerr-de Sitter Kerr
SchwarzschildSchwarzschild-de Sitter
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Test particle motion Basic features
• ergosphere
• static radius
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Test particle motion Kerr-de Sitter
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Test particle motion Schwarzschild-de Sitter
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Test spinning particle motion
[Stuchlik, Acta Phys. Slovaca (49),1999][Stuchlik and Kovar, Class. Quantum Grav. (23), 2006]
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Test spinning particle motion
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Perfect fluid equilibrium configurations
[Stuchlik, Slany and Hledik, Astronomy and Astrophysics (363), 2000][Slany and Stuchlik, Class. Quantum Grav. (22), 2005]
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Perfect fluid equilibrium configurations
W=const. contours
W-behaviour (equatorial plane)
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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)
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• 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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Thank you