Conformally Flat Space-Time with Dust Matter in f(R) Gravity

Abstract

In this study, conformally flat space-times filled with dust matter is investigated in framework of f(R) gravitation theory. Exact solutions and field equations of conformally flat space-time in the presence of dust matter are obtained without using any restrictive method and approximation. It is shown that conformally flat space-times in framework of f(R) gravitation theory permit to dust matter with constant energy density. f(R) function which characterise dynamic structure of theory is obtained from solutions of field equations for constructed model. Obtained f(R) function for constructed model and viable f(R) functions, which are used to express various conditions and situations in theory, are compared. Change of the metric potential with respect to radial coordinate is examined by the help of graphic and limiting cases of the solutions are investigated. Finally, obtained results are discussed in the terms of physical and geometric aspects.    

Keywords

• f(R) gravitation theory,Dust matter,Conformal space-time

f(R) Gravitasyon Teorisinde Toz Bulutlu Konformal Düz Uzay-Zamanlar

Abstract

Bu çalışmada, toz bulutu bulunan konformal düz uzay-zamanlar f(R) gravitasyon teorisi çerçevesinde incelenmiştir. Toz bulutu varlığında konformal düz uzay-zamanların alan denklemleri ve tam çözümleri herhangi bir yaklaşım ve kısıtlayıcı metot kullanılmadan elde edilmiştir. f(R) gravitasyon teorisi çerçevesinde konformal düz uzay-zamanların sabit enerji yoğunluklu toz bulutu varlığına izin verdiği gösterilmiştir.  Teorinin dinamik yapısını karakterize eden f(R) fonksiyonu oluşturulan model için alan denklemlerinin çözümlerinden elde edilmiştir. Oluşturulan model için elde edilen f(R) fonksiyonu ile teoride farklı koşul ve durumları ifade etmek için kullanılan uygulanabilir f(R) fonksiyonları karşılaştırılmıştır. Metrik potansiyelin radyal koordinata göre değişimi grafik yardımıyla irdelenmiş ve çözümlerin sınır durumları incelenmiştir. Son olarak, elde edilen sonuçlar fiziksel ve geometrik açıdan irdelenerek tartışılmıştır.    

Keywords

• f(R) Gravitasyon Teorisi,Toz Madde,Konformal uzay-zaman

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