Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10408364" target="_blank" >RIV/00216208:11320/19:10408364 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=B_hDrz~TVD" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=B_hDrz~TVD</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1103/PhysRevD.100.103013" target="_blank" >10.1103/PhysRevD.100.103013</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method
Popis výsledku v původním jazyce
Motivated by black holes surrounded by accretion structures, we consider in this series static and axially symmetric black holes "perturbed" gravitationally as being encircled by a thin disc or a ring. In previous papers, we employed several different methods to detect, classify, and evaluate chaos which can occur, due to the presence of the additional source, in timelike geodesic motion. Here we apply the Melnikov-integral method, which is able to recognize how stable and unstable manifolds behave along the perturbed homoclinic orbit. Since the method standardly works for systems with 1 degree of freedom, we first suggest its modification applicable to 2 degrees of freedom (which is our case), starting from a suitable canonical transformation of the corresponding Hamiltonian. The Melnikov function reveals that, after the perturbation, the asymptotic manifolds tend to split and intersect, consistent with the chaos found by other methods in previous papers.
Název v anglickém jazyce
Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method
Popis výsledku anglicky
Motivated by black holes surrounded by accretion structures, we consider in this series static and axially symmetric black holes "perturbed" gravitationally as being encircled by a thin disc or a ring. In previous papers, we employed several different methods to detect, classify, and evaluate chaos which can occur, due to the presence of the additional source, in timelike geodesic motion. Here we apply the Melnikov-integral method, which is able to recognize how stable and unstable manifolds behave along the perturbed homoclinic orbit. Since the method standardly works for systems with 1 degree of freedom, we first suggest its modification applicable to 2 degrees of freedom (which is our case), starting from a suitable canonical transformation of the corresponding Hamiltonian. The Melnikov function reveals that, after the perturbation, the asymptotic manifolds tend to split and intersect, consistent with the chaos found by other methods in previous papers.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10300 - Physical sciences
Návaznosti výsledku
Projekt
<a href="/cs/project/GA17-13525S" target="_blank" >GA17-13525S: Zdroje silné gravitace a jejich astrofyzikální význam</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Physical Review D
ISSN
2470-0010
e-ISSN
—
Svazek periodika
100
Číslo periodika v rámci svazku
10
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
16
Strana od-do
103013
Kód UT WoS článku
000496926600002
EID výsledku v databázi Scopus
2-s2.0-85075271002