10 research outputs found
Separability and Hidden Symmetries of Kerr-Taub-NUT Spacetime in Kaluza-Klein Theory
The Kerr-Taub-NUT spacetime in the Kaluza-Klein theory represents a localized
stationary and axisymmetric object in four dimensions from the Kaluza-Klein
viewpoint. That is, it harbors companion electromagnetic and dilaton fields,
thereby showing up the signature of the extra fifth dimension. We explore the
separability structure of this spacetime and show that the Hamilton-Jacobi
equation for geodesics admits the complete separation of variables only for
massless geodesics. This implies the existence of the hidden symmetries in the
spacetime, which are generated by the conformal Killing tensor. Using a simple
trick built up on a conformally related metric (an "effective" metric) with the
Killing tensor, we construct the explicit expression for the conformal Killing
tensor.Comment: 10 pages; REVTe
2-Formilpiridin N(4)-Metil Tiyosemikarbazon Ve 2-Asetilpiridin N(4)-Etil Tiyosemikarbazon Moleküllerinin Teorik Olarak İncelenmesi
Bu çalışmada (HFo4M) 2-Formilpiridin N(4)-metil tiyosemikarbazon (C8H10N4S) ve (HAc4E) 2-Asetilpiridin N(4)-etil tiyosemikarbazon (C10H14N4S) moleküllerinin yapısal, spektroskopik, elektronik ve doğrusal olmayan optik özellikleri kuantum kimyasal hesaplamaları metodları kullanılarak incelendi. Optimize edilmiş geometri için hesaplanan teorik sonuçlar deneysel değerler ile karşılaştırıldı ve oldukça uyum içinde oldukları görüldü. HFo4M ve HAc4E molekülleri için statik yüksek mertebe kutuplanabilirlik parametreleri sırayla 23.6815×10-30 ve 20.838×10-30 esu olarak elde edilmiş ve doğrusal olmayan optik malzemeler için umut verici bir aday olduğu görülmüştür. HFo4M ve HAc4E molekülleri için B3LYP yöntemi ile 2.1630 ve 2.2556 eV olarak hesaplanan HOMO ve LUMO arasındaki enerji aralıklarının nispeten düşük olması doğrusal olmayan optik özelliklerin belirgin olmasına katkı sağladığı görülmüştür
Hidden symmetries and geodesics of Kerr spacetime in Kaluza-Klein theory
The Kerr spacetime in Kaluza-Klein theory describes a rotating black hole in
four dimensions from the Kaluza-Klein point of view and involves the signature
of an extra dimension that shows up through the appearance of the electric and
dilaton charges. In this paper, we study the separability properties of the
Hamilton-Jacobi equation for geodesics and the associated hidden symmetries in
the spacetime of the Kerr-Kaluza-Klein black hole. We show that the complete
separation of variables occurs only for massless geodesics, implying the
existence of hidden symmetries generated by a second rank conformal Killing
tensor. Employing a simple procedure built up on an "effective" metric, which
is conformally related to the original spacetime metric and admits a complete
separability structure, we construct the explicit expression for the conformal
Killing tensor. Next, we study the properties of the geodesic motion in the
equatorial plane, focusing on the cases of static and rotating Kaluza-Klein
black holes separately. In both cases, we obtain the defining equations for the
boundaries of the regions of existence, boundedness and stability of the
circular orbits as well as the analytical formulas for the orbital frequency,
the radial and vertical epicyclic frequencies of the geodesic motion.
Performing a detailed numerical analysis of these equations and frequencies, we
show that the physical effect of the extra dimension amounts to the significant
enlarging of the regions of existence, boundedness and stability towards the
event horizon, regardless of the classes of orbits.Comment: 25 pages, 5 figures; REVTe