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

Year 2019, Volume: 23 Issue: 1, 59 - 65, 01.04.2019

Doğukan Taşer

https://doi.org/10.19113/sdufenbed.442768

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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