五维时空中宇宙项和宇宙解的相关研究

发布时间：2018-03-22 09:08

本文选题：Brans-Dicke理论　切入点：动力学方程　出处：《武汉科技大学》2010年硕士论文　论文类型：学位论文

【摘要】：本文根据增加维数和改变引力常数G两种手段,将四维宇宙的计算方法推广到五维时空,得到五维宇宙中的Robertson-Walker度规.在此度规下,通过约束□φ=f(φ)与Λ=Λ(φ)得到宇宙项与质量的关系,进一步通过五维与四维场方程的比较得到宇宙项与能量之间的关系,并得出k =0,±1时宇宙动力学方程的解和测地线方程的解.最后将五维爱因斯坦张量分解成四维爱因斯坦张量和一个与能量—动量张量有关的剩余量H ab,得到理想流体状态方程. 本文共分为五个章节: 第一章,本章介绍了Brans-Dicke理论产生的背景,空—时—质理论的基本形式和变引力常数产生的背景. 第二章,本章利用增加维数的方法将四维宇宙时空推广到五维宇宙时空,得到五维宇中的Robertson-Walker度规.通过进一步计算得到了宇宙项与质量和宇宙项与能量之间的关系. 第三章,本章在假设物质场和BD标量场是同质的情况下,得到k =0,±1时宇宙动力学方程的解和平直空间下的宇宙解,接着对五维测地线方程进行讨论. 第四章,本章利用将五维爱因斯坦张量分解成四维爱因斯坦张量和与能量—动量张量有关的剩余量H ab,得到理想流体状态方程. 第五张,总结.
[Abstract]:In this paper, by means of increasing the dimension and changing the gravitational constant G, the calculation method of the four-dimensional universe is extended to the five-dimensional spacetime, and the Robertson-Walker metric in the five-dimensional universe is obtained. Under this metric, the relation between the cosmological term and the mass is obtained by constraining-蠁 f (蠁) and A = A (蠁). By comparing the five dimensional and four dimensional field equations, the relationship between the cosmic term and the energy is obtained. The solution of the kinetic equation of the universe and the solution of the geodesic equation are obtained. Finally, the five-dimensional Einstein Zhang Liang is decomposed into four-dimensional Einstein Zhang Liang and a residual quantity H _ ab-related to energy-momentum Zhang Liang, and the ideal fluid state equation is obtained. This paper is divided into five chapters:. In the first chapter, the background of Brans-Dicke theory, the basic form of space-time-mass theory and the background of variable gravitational constant are introduced. In the second chapter, by using the method of increasing dimension, we generalize the space and time of the four-dimensional universe to the space-time of the five-dimensional universe, and obtain the Robertson-Walker metric in the five-dimensional universe. The relation between the cosmic term and the mass, the term of the universe and the energy is obtained by further calculation. In chapter 3, under the assumption that the matter field and BD scalar field are homogeneous, we obtain the solutions of the kinetic equation k ~ (0, 卤1) and the cosmic solution in a flat space. Then we discuss the five dimensional geodesic equation. In the fourth chapter, the ideal fluid equation of state is obtained by decomposing five dimensional Einstein Zhang Liang into four dimensional Einstein Zhang Liang and the residue H abs related to energy-momentum Zhang Liang. 5th, summary.
【学位授予单位】：武汉科技大学
【学位级别】：硕士
【学位授予年份】：2010
【分类号】：P159

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