Solution of the Dirac equation in the non-asymptotically flat geometries
Başlık çevirisi mevcut değil.
- Tez No: 513575
- Danışmanlar: Prof. Dr. MUSTAFA HALİLSOY
- Tez Türü: Doktora
- Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2005
- Dil: İngilizce
- Üniversite: Doğu Akdeniz Üniversitesi-Eastern Mediterranean University
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 61
Özet
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Özet (Çeviri)
This thesis is devoted to the solution of the Dirac equation in the two nonasymptotically flat geometries; the Bertotti-Robinson (BR) geometry and the near horizon (NH) geometry of an extreme Kerr black hole (BH), respectively. While the Dirac equation with charge coupling is considered in the uniform electromagnetic field space of BR, in the NH geometry, the test Dirac i.e., Chandrasekhar-Dirac (CD) equation is used. The methods of separation of variables and decoupling are achieved for each geometry. In the BR geometry, the solution of angular equation is given both in terms of Jacobi polynomials and of spin-weighted spheroidal harmonics. The separated axial equation is reduced to a rare Riccati type of differential equation. In the neutrino (massless and chargeless particles) case, it is shown that the axial equation takes the from of a hypergeometric differential equation. Unlike the BR geometry, the angular equation depends on the mass, while the axial equation turns out to be independent of the mass and is exactly solved in the NH geometry. The angular equation, in the neutrino case, reduces to a confluent Heun equation. In general for a massive case, the angular equation is expressible at best, as a set of coupled first order differential equations apt for numerical investigation. For each geometry, the axial potentials corresponding to the associated Schrödinger-type wave equations and their conserved currents are found. The thesis concludes with a verification of the absence of superradiance for Dirac particles in the NH geometry, a result which is well known within the context of general Kerr background.
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