弯曲时空中的多普勒效应

发布时间：2018-04-11 21:20

本文选题：广义相对论 + 多普勒效应　；参考：《湖南师范大学》2014年硕士论文

【摘要】：相对论性效应是天体物理学和理论物理学中一个非常重要的研究领域,对各种相对论性效应的理论研究可以帮助我们解释某些天文观测现象。本文主要研究两种相对论性效应：(1)多普勒效应,(2)引力场中的引力频移(我们称之为弯曲空间的多普勒效应)。多普勒效应是波源和观察者有相对运动时,观察者接受到波的频率与波源发出的频率并不相同的现象。相对论性多普勒效应是根据狭义相对论理论,研究了传播速度接近于光速的波动因为波源与观察者的相对运动而使得其频率(以及波长)的变化。相对论性多普勒效应和非相对论性的多普勒效应有许多不同之处,其方程式考虑了狭义相对论中的时间延长效应。这些方程式描述的是所观察到的频率的总差值,并具有相对论要求的洛仑兹对称性。我们研究了狭义相对论的多普勒效应,并给出了广义相对论的多普勒效应的一般表达式。在物理学中,当观测者在较弱引力场区域观测时,来自较强引力场区域的光或者其它形式的辐射的波长会变长,这种效应叫做引力红移。相反地,当观测者在较强引力场区域观测时,来自于较弱引力场区域的光或者其它形式的辐射的波长会变短,这种效应叫做引力蓝移。引力红移和引力蓝移统称为引力频移。本文研究了几种引力场中的引力频移现象：(1)在Schwarzschild引力场中,我们研究了其引力红移,所得到的结果与对太阳的光谱频率的观测到的引力红移一致；(2)在Reissner-Nordstrom引力场中,我们研究了电荷对频移的影响,得到场源所含电荷对频移的影响与电荷的正负无关；(3)在Kerr引力场中,我们讨论了时空的角动量对频移的影响,得到频移效应不仅与场源的质量有关,而且与时空的角动量有关；(4)在引力波时空中,其频移是时间的函数,而且频移依赖于光信号在引力波场中的传播方向。
[Abstract]:Relativistic effect is a very important research field in astrophysics and theoretical physics. The theoretical study of various relativistic effects can help us to explain some astronomical observation phenomena.In this paper, we mainly study two relativistic effects: 1) Doppler effect and 2) the frequency shift of gravity in gravitational field (we call it Doppler effect in curved space.Doppler effect is a phenomenon that the frequency of the wave received by the observer is different from that of the source when the source and the observer are in relative motion.The relativistic Doppler effect is based on the theory of special relativity to study the variation of the frequency (as well as the wavelength) due to the relative motion of the source and the observer.There are many differences between the relativistic Doppler effect and the non-relativistic Doppler effect, whose equation takes into account the time prolongation effect in the special relativity.These equations describe the total difference of observed frequencies and have the Lorentz symmetry required by relativity.We study the Doppler effect of the special relativity and give the general expression of the Doppler effect of the general relativity.In physics, the wavelength of light or other forms of radiation from a stronger gravitational field becomes longer when observers observe it in a region with a weaker gravitational field. This effect is called gravitational redshift.On the contrary, the wavelength of light or other forms of radiation from the weaker gravitational field becomes shorter when the observer observes the region of the stronger gravitational field. This effect is called gravitational blue shift.Gravitational red shift and gravitational blue shift are called gravitational frequency shift.In this paper, we have studied the gravitational frequency shift phenomenon in several gravitational fields: 1) in the Schwarzschild gravitational field, we have studied its gravitational redshift. The results obtained are consistent with the observed gravitational redshift of the solar spectral frequency. (2) in the Reissner-Nordstrom gravitational field,We have studied the effect of charge on frequency shift. We have obtained that the influence of charge in field source on frequency shift is independent of the positive or negative charge. In the Kerr gravitational field, we discuss the influence of angular momentum of space-time on frequency shift.It is obtained that the frequency shift effect is not only related to the mass of the field source, but also to the angular momentum of space-time. In the gravitational wave space-time, the frequency shift is a function of time, and the frequency shift depends on the direction of the light signal propagating in the gravitational wave field.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P131

【参考文献】