Gravitomagnetism in general relativity and massive gravity

---

Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Fizik Bölümü, Türkiye

Tezin Onay Tarihi: 2014

Öğrenci: GÖKÇEN DENİZ ÖZEN

Danışman: BAYRAM TEKİN

Özet:

In this thesis gravitomagnetic effects are analysed in some detail. Einstein’s equations for weak gravitational fields are derived. Using appropriate gauge fixings, metric perturbation is decomposed and degrees of freedom are identified. Physical degrees of freedom are chosen and it is proven that they characterize the propagation of gravitational waves. Production of gravitational waves is demonstrated as well as their effects on the polarization of test particles. Analogs of the Maxwell’s equations are derived for gravity. From the analysis of the scattering amplitude, potential energy is found for massive and massless gravity theories, the appropriate spin alignment for minimum potential energy is calculated and the difference between general relativity and the massive gravity for this spin alignment is shown. In the Appendix, some useful calculations are given. Save for some details in the computations, no originality in this thesis is claimed. Somewhat standard material about weak field gravity, gauge fixings and degree of freedom counting follows closely the discussion in Chapter 7 of Carroll's excellent book. Chapter 2 of the thesis closely follows Harris's paper "Analogy between general relativity and electromagnetism for slowly moving particles in weak gravitational fields". Chapter 3 of this thesis is a review of the paper Güllü-Tekin "Spin–spin interactions in massive gravity and higher derivative gravity theories".