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研究生: 馮維祥
Feng, Wei-Xiang
論文名稱: 中子星的R平方重力模型:數值研究
R-squared Gravity on Neutron Star: Numerical Study
指導教授: 耿朝強
Geng, Chao-Qiang
口試委員: 高文芳
何小剛
倪維斗
張維甫
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 56
中文關鍵詞: 重力修正理論中子星狀態方程式TOV方程式
外文關鍵詞: modified gravity, neutron star, equation of state, TOV equation
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  • 迄今,中子星的狀態方程式仍然尚未有定論。由於在廣義相對論裡面探討緻密星體時,狀態方程式一般都從粒子物理以及統計力學的觀點算出而不與廣義相對論直接相關,因此廣義相對論對可行的狀態方程式限制不大。

    在這文章中,我們希望能從考慮R平方(Starobinsky)重力模型 f(R) = R + αR^2 及其所得出之修正的Tolman-Oppenheimer-Volkoff(TOV)方程式進而給出可行的狀態方程式多一些限制,而非以粒子和統計物理為出發點考慮此問題。


    Until now, the equation of state of the neutron star is still an open question. Since the equation of state is usually derived from the starting point of particle physics and statistical mechanics when studying the compact star under the scheme of General Relativity (GR), GR doesn’t impinge on the physical equation of state directly.
    In this work, we consider the R-squared (Starobinsky) model of gravity f(R) = R + αR^2 and obtain the modified TOV equation in an attempt to give more constraints on the equation of state rather than the standard GR scheme.

    Abstract v Chinese Abstract vii Acknowledgments ix Contents xi List of Figures xiii 1 Introduction 1 1.1 R-squared model ...................................................................................... 1 1.2 Neutron star ............................................................................................. 2 2 Calculations and Numerical Set-up 3 2.1 Field equations implemented..................................................................... 3 2.2 Numerical set-up .................................................................................... 10 2.3 Boundary conditions ............................................................................... 14 3 Numerical Procedure and Results 17 3.1 R ̄andR ̄′at the boundary of the star ......................................................... 17 3.1.1 Constant density case through out the interior .................................... 18 3.1.2 Simple polytropic case ........................................................................ 19 3.2 Constraint on α and the equation of state (EoS) ...................................... 20 3.2.1 A reasonable determination of α ̄ ........................................................ 21 3.2.2 Finding the reasonable EoS ................................................................. 25 4 Conclusions and Outlook 29 Bibliography 31 Appendix 33 A Conventions and Units 33 B Variation on Metric f(R) gravity 35 C EoM for static perfect fluid 37 D Profiles for various values of α ̄ : 0.01, 0.005, 0.002, 0.001, 0.0005, 0.0002 41 Last Note 55

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