influence of cosmological constant on particle dynamics near compact objects zdeněk stuchlík, petr...

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

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 Sitter Kerr

SchwarzschildSchwarzschild-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:0803.3641)

• 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

Thank you