Simetrik paralel kütle-çekiminde statik, silindirik simetrik çözümler
Küçük Resim Yok
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Tekirdağ Namık Kemal Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tezde, Genel Görelilik (GG) ile aralarında e¸sde?gerlilik oldu?gu ispat edilen ve "Simetrik Teleparallel (STEGR)" olarak adlandırılan teoeriden yola çıkarak, GG'ye alternatif ve STEGR'nin genelle¸stirilmi¸s hali olan f (Q) kütle-çekimi çalı¸sıldı. Ayrıca bu tezde, bugüne kadar statik, silindirik simetrik uzay-zamanda incelenmemi¸s olan f (Q) teori, bu uzay-zamanda incelenerek bu teorinin tutarlılı?gı irdelenmi¸stir. GG'deki Ricci skalerinin f (Q) teorideki kar¸sılı?gı olan Q non-metrisiti skalerini elde edebilmek amacıyla, en genel statik, silindirik simetrik metrikten non-metrisiti, disformasyon ve süper potansiyel tensör bile¸senleri hesaplandı. Vakum çözümlerinde, elde edilen alan denklemlerine göre f (Q) sıfır olması gerekirken, ideal akı¸skan çözümlerinde vakum çözümlerinden ve literatürde çokça incelenen küresel simetrik çözümlerden farklı olarak f (Q) ve Q skalerini kısıtlayıcı bir durum bulunmamaktadır. Bu durum do?grultusunda, en genel sonucu elde edebilmek için, f (Q) fonksiyonu, hem daha önceki kozmolojik çözümlerle hem de en basit haliyle kuvvet serisi olarak seçilerek aksiyon denklemi olu¸sturuldu. Aksiyonun metri?ge ve efayna göre varyasyonundan elde edilen alan denklemleri, anizotropik ideal akı¸skan için enerji-momentum tensörü e¸sitli?gi kullanılarak, enerji yo?gunlu?gu ? ve yönelimli basınçlar pm elde edildi. Bilinen statik silindirik simetrik uzay-zaman çözümleri kullanılarak, bu çözümlerin f (Q) teorisindeki kar¸sılıkları elde edilmi¸stir. Pozitif enerji yo?gunlu?gunu verecek sabitler belirlenerek, yönlü basınçların sayısal de?gerleri elde edilerek grafikleri analiz edilmi¸stir. Öte taraftan, elde edilen çözümlerin tutarlılı?gını analiz etmeyi sa?glayan enerji ko¸sulları, bo¸s enerji ko¸sulu (NEC), zayıf enerji ko¸sulu (WEC), dominant enerji ko¸sulu (DEC) ve güçlü enerji ko¸sulu (SEC) e¸sitsizlikleri hesaplanarak, pozitif enerji yo?gunlu?gu katsayılarında davranı¸sları grafiklendirilmi¸stir.
In this thesis, based on the theorem called 'Symmetric Teleparallel (STEGR)', which has been shown to be equivalent to General Relativity (GR), f (Q) gravity is studied, which is an alternative to GR and a generalised version of STEGR. Additionally, f (Q) theory, which has not been previously examined in a static, cylindrically symmetric spacetime, was investigated in this spacetime to assess the consistency of this theory. In order to obtain the non-metricity scalar Q for f (Q) theory, which corresponds to the Ricci scalar in GR, the components of non-metricity, disformation, and superpotential tensors were calculated from the most general static, cylindrically symmetric metric. According the field equations, f (Q) should be zero in vacuum solutions. However, unlike the vacuum solutions and the widely studied spherically symmetric solutions in the literature, there are no constraints on the scalar Q and the function f (Q) in perfect fluid solutions. In this regard, to obtain the most general result, the f (Q) function was chosen as a power series which is both coherent with cosmological solutions and in its simplest form, and equation of action was constructed accordingly. The energy density ? and the directional pressures pm are obtained by the field equations which are derived from the variation of the action with respect to metric and affine connections and the energy momentum tensor of the anisotropic perfect fluid. Corresponding solutions of f (Q)-gravity are discussed for few known solutions of static, cylindrically symmetric spacetime. By determining the constants that would provide positive energy density, the numerical values of the directional pressures were obtained, and the graphs were analyzed accordingly. Furthermore, to analyze the consistency of the obtained solution, the energy conditions null energy condition (NEC), weak energy condition (WEC), dominant energy condition (DEC), and strong energy condition (SEC) inequalities were calculated, and their behaviors were graphed on positive energy density coefficients.
In this thesis, based on the theorem called 'Symmetric Teleparallel (STEGR)', which has been shown to be equivalent to General Relativity (GR), f (Q) gravity is studied, which is an alternative to GR and a generalised version of STEGR. Additionally, f (Q) theory, which has not been previously examined in a static, cylindrically symmetric spacetime, was investigated in this spacetime to assess the consistency of this theory. In order to obtain the non-metricity scalar Q for f (Q) theory, which corresponds to the Ricci scalar in GR, the components of non-metricity, disformation, and superpotential tensors were calculated from the most general static, cylindrically symmetric metric. According the field equations, f (Q) should be zero in vacuum solutions. However, unlike the vacuum solutions and the widely studied spherically symmetric solutions in the literature, there are no constraints on the scalar Q and the function f (Q) in perfect fluid solutions. In this regard, to obtain the most general result, the f (Q) function was chosen as a power series which is both coherent with cosmological solutions and in its simplest form, and equation of action was constructed accordingly. The energy density ? and the directional pressures pm are obtained by the field equations which are derived from the variation of the action with respect to metric and affine connections and the energy momentum tensor of the anisotropic perfect fluid. Corresponding solutions of f (Q)-gravity are discussed for few known solutions of static, cylindrically symmetric spacetime. By determining the constants that would provide positive energy density, the numerical values of the directional pressures were obtained, and the graphs were analyzed accordingly. Furthermore, to analyze the consistency of the obtained solution, the energy conditions null energy condition (NEC), weak energy condition (WEC), dominant energy condition (DEC), and strong energy condition (SEC) inequalities were calculated, and their behaviors were graphed on positive energy density coefficients.
Açıklama
Fen Bilimleri Enstitüsü, Fizik Ana Bilim Dalı
Anahtar Kelimeler
Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
