Unit:
Department of PhysicsLibrary of the School of Science
Dissertation committee:
Θεοχάρης Αποστολάτος, Αναπληρωτής Καθηγητής, Τμήμα Φυσικής, ΕΚΠΑ (κύριος επιβλέπων)
Πέτρος Ιωάννου, Καθηγητής, Τμήμα Φυσικής, ΕΚΠΑ
Νικόλαος Στεργιούλας, Καθηγητής, Τμήμα Φυσικής, ΑΠΘ
Νεκτάριος Βλαχάκης, Αναπληρωτής Καθηγητής, Τμήμα Φυσικής, ΕΚΠΑ
Γεώργιος Διαμάντης, Αναπληρωτής Καθηγητής, Τμήμα Φυσικής, ΕΚΠΑ
Δημήτριος Φραντζεσκάκης, Καθηγητής, Τμήμα Φυσικής, ΕΚΠΑ
Γεώργιος Παππάς, Επίκουρος Καθηγητής, Τμήμα Φυσικής, ΑΠΘ
Original Title:
Μελέτη των ιδιοτήτων των τροχιών γύρω από μελανές οπές Kerr με τη χρήση νευτώνειων αναλόγων
Translated title:
Study of the properties of the orbits around a Kerr Black Hole using Newtonian analogues
Summary:
This PhD thesis aims to demonstrate the similarity of a particular Newtonian gravitational field, namely the gravitational field of Euler produced by two point masses, at a fixed distance from each other, with the gravitational field of a Kerr black hole. At a first glance, the similarity seems simply superficial and many things relating the two problems were completely unknown. Only some indirect references to some common properties of the two fields were mentioned in the literature.
The purpose of this study is to use this similarity to study difficult orbital characteristics in a Kerr black hole, by analyzing corresponding orbits in the analogous Newtonian gravitational field.
We have studied this particular Newtonian gravitational field, the Euler field, by Hamilton-Jacobi method, in order to separate it in appropriate coordinates and construct the three integrals of motion corresponding to this problem.
We have derived the relationships that relate the expressions for the third integral of the motion as calculated by Landau, Lynden-Bell and a third version, of it, which seems to match the Carter constant, which is introduced naturally in the analysis of the orbits in the Kerr metric.
Subsequently, we identified the similarity of the potentials that govern the radial and polar motion of the orbits at Euler and Kerr potential.
Next, we followed the method of action angle variables to detect the fundamental frequencies of the orbits in Kerr metric, in order to calculate for each orbit with specific orbital characteristics the corresponding fundamental frequencies that characterize the orbit. These frequencies are the directly observed quantities in the case of Kerr black holes when the orbits are associated with the emission of gravitational waves radiated from such a source.
Next, we prove that some particular characteristics of Kerr orbits show up in the Euler problem,, as well. Namely, the fact that there are pairs of completely different orbits characterized by the exactly the same set of frequencies.
Therefore the frequency-orbit relationship is not one-to-one correspondent.
Finally, we have studied the stability of spherical orbits (orbits with zero eccentricity) under the act of a dissipative force, corresponding to the self-force of relativistic orbits when the gravitational radiation of the orbiting body is taken into account. In Kerr case, no initial conditions suitable for such resonance were found (in accordance with the relevant literature). However, in the Euler field, suitable initial conditions were found that satisfy the required resonance condition. These orbits, though initially spherical, become eccentric over time.
In fact, we have managed to build a theoretical model
which interprets the evolution of the initially
spherical orbits, whether or not they meet a resonance.
Main subject category:
Science
Keywords:
Euler problem, black holes, separability and integrability, self force, resonance, circular orbits, non-integrability
