Born-infeld gravity theories in D-dimensions

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Tezin Türü: Doktora

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

Tezin Onay Tarihi: 2012

Öğrenci: TAHSİN ÇAĞRI ŞİŞMAN

Danışman: BAYRAM TEKİN

Özet:

Born-Infeld gravity proposed by Deser and Gibbons takes its origin from two ideas: Born-Infeld electrodynamics and Eddington's gravitational action. The theory is defined with a determinantal action involving the Ricci tensor as in the Eddington's theory; however, in contrast, the independent variable is the metric as in Einstein's gravity and the action is constructed in analogy with the action of the Born-Infeld electrodynamics. Main challenge in defining a Born-Infeld type gravity is obtaining a unitary theory around--at least--flat and maximally symmetric constant curvature backgrounds. In this thesis, a framework for analyzing the tree-level unitarity of a generic D-dimensional Born-Infeld type gravity is developed. Besides, in three dimensions, a Born-Infeld gravity theory which is unitary to all orders in the curvature is studied in detail. This theory was introduced as an extension of a specific quadratic curvature gravity theory dubbed as ``new massive gravity'' which is unitary with a massive spin-2 excitation in its spectrum. Besides having a unitary massive spin-2 excitation, the Born-Infeld gravity in three dimensions has a holographic $c$-function which is the same as Einstein's gravity. In addition, the theory has constant curvature Type-N and Type-D solutions which are the same as the cosmological topologically massive gravity.