Y (R)F²Gravitasyon modelinin düzgün kara delik Çözümleri

Abstract

Bu tezde ilk olarak d ³ cebir ile ilgili temel kavramlar ve diferansiyel formlar n özellikleri incelendi. Daha sonra, Einetein' n Genel Relativite teorisi ve Einstein-Maxwell teorisi diferansiyel formlarla ifade edildi. Minimal olmayan Einstein-Maxwell teori olarak ta bilinen, gravitasyonun elektromanyetik alana minimal olmayan ba§lanmalar n içeren model ele al nd ve bu modele küresel simetrik statik bir metrik için, düzgün karadelik çözümleri bulunarak, bu çözümlerin enerji ko³ullar n sa§lay p sa§lamad § ara³t r ld . Bunun sonucu olarak bu çözümlerin yüklü karadeliklerle birlikte bir dulite dönü³ümüyle manyetik monopol yüküne sahip kara delikleri de tarif edebildi§i görüldü.

In this thesis, the basic concepts related with the exterior algebra and the features of the di erential forms have been rstly investigated. Then, Einstein's theory of gravity and Einstein-Maxwell theory have been expressed in di erential forms. By dealing with the model known as non-minimal Einstein-Maxwell theory which involves the non-minimal couplings between the electromagnetic elds and gravitational eld has been considered. By nding regular black hole solutions to the model for spherically symmetric static metric, it has been investigated about whether these solutions satisfy energy conditions or not. As a result, it was shown that these solutions can described the black holes with electric charge, and also magnetic monopole charge by a duality transformation.