Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985815%3A_____%2F19%3A00520556" target="_blank" >RIV/67985815:_____/19:00520556 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1103/physrevd.100.103013" target="_blank" >https://doi.org/10.1103/physrevd.100.103013</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevD.100.103013" target="_blank" >10.1103/PhysRevD.100.103013</a>

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

<a href="/cs/project/GJ17-06962Y" target="_blank" >GJ17-06962Y: Nelineární jevy ve vícekanálové astronomii černých děr</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Physical review D

ISSN

2470-0029

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