3 research outputs found
Orbitální dynamika v okolí černé díry obklopené hmotou
This thesis studies the dynamics of geodesic motion within a curved spacetime around a Schwarzschild black hole, perturbed by a gravitational field of a far axisymmetric dis- tribution of mass enclosing the system. This particular spacetime can serve as a versatile model for a diverse range of astrophysical scenarios. At the beginning of the thesis, a brief overview of the theory of classical mechanical systems and properties of geodesic motion are provided. A brief introduction to the theory of integrability and non-integrability, along with essential tools for analysis of non-integrable systems, including Poincaré sur- face of section and rotation numbers, is provided as well. These methods are subsequently applied to the under study spacetime through numerical methods. By utilising the rota- tion numbers, the widths of resonances are calculated, which are then used in establishing the relation between the perturbation parameter and the parameter characterising the perturbed metric. 1Táto práca študuje dynamiku geodetického pohybu v zakrivenom priestoročase okolo Schwarzschildovej čiernej diery, perturbovanej gravitačným poľom vzdialenej osovo sy- metrickej distribúcie hmoty obklopujúcej systém. Tento konkrétny priestoročas môže slúžiť ako všestranný model pre rôznorodé astrofyzikálne scenáre. V úvode práce je poskytnutý stručný prehľad teórie klasických mechanických systémov a vlastností geodet- ického pohybu. Taktiež je poskytnuté stručné uvedenie do teórie integrability a neinte- grability spolu s podstatnými nástrojmi pre analýzu neintegrabilných systémov, zahrňu- júc Poincarého rezy a rotačné čísla. Tieto metódy sú následne aplikované na skúmaný priestoročas pomocou numerických metód. Využitím rotačných čísel sú vypočítané šírky rezonancií, ktoré sú neskôr použité k stanoveniu vzťahu medzi pertubačným parametrom a parametrom charakterizujúcim perturbovanú metriku. 1Institute of Theoretical PhysicsÚstav teoretické fyzikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
Growth of orbital resonances around a black hole surrounded by matter
This work studies the dynamics of geodesic motion within a curved spacetime
around a Schwarzschild black hole, perturbed by a gravitational field of a far
axisymmetric distribution of mass enclosing the system. This spacetime can
serve as a versatile model for a diverse range of astrophysical scenarios and,
in particular, for extreme mass ratio inspirals as in our work. We show that
the system is non-integrable by employing Poincar\'e surface of section and
rotation numbers. By utilising the rotation numbers, the widths of resonances
are calculated, which are then used in establishing the relation between the
underlying perturbation parameter driving the system from integrability and the
quadrupole parameter characterising the perturbed metric. This relation allows
us to estimate the phase shift caused by the resonance during an inspiral.Comment: 11 pages, 3 figures, 1 table, Proceedings of RAGtime 23-25. Edited by
Z. Stuchl\'ik, G. T\"or\"ok and V. Karas. Institute of Physics in Opav
Orbital dynamics around a black hole surrounded by matter
This thesis studies the dynamics of geodesic motion within a curved spacetime around a Schwarzschild black hole, perturbed by a gravitational field of a far axisymmetric dis- tribution of mass enclosing the system. This particular spacetime can serve as a versatile model for a diverse range of astrophysical scenarios. At the beginning of the thesis, a brief overview of the theory of classical mechanical systems and properties of geodesic motion are provided. A brief introduction to the theory of integrability and non-integrability, along with essential tools for analysis of non-integrable systems, including Poincaré sur- face of section and rotation numbers, is provided as well. These methods are subsequently applied to the under study spacetime through numerical methods. By utilising the rota- tion numbers, the widths of resonances are calculated, which are then used in establishing the relation between the perturbation parameter and the parameter characterising the perturbed metric.