本文選題：廣義相對論 + 多普勒效應(yīng)　； 參考：《湖南師范大學(xué)》2014年碩士論文

【摘要】：相對論性效應(yīng)是天體物理學(xué)和理論物理學(xué)中一個非常重要的研究領(lǐng)域,對各種相對論性效應(yīng)的理論研究可以幫助我們解釋某些天文觀測現(xiàn)象。本文主要研究兩種相對論性效應(yīng)：(1)多普勒效應(yīng),(2)引力場中的引力頻移(我們稱之為彎曲空間的多普勒效應(yīng))。 多普勒效應(yīng)是波源和觀察者有相對運動時,觀察者接受到波的頻率與波源發(fā)出的頻率并不相同的現(xiàn)象。相對論性多普勒效應(yīng)是根據(jù)狹義相對論理論,研究了傳播速度接近于光速的波動因為波源與觀察者的相對運動而使得其頻率(以及波長)的變化。相對論性多普勒效應(yīng)和非相對論性的多普勒效應(yīng)有許多不同之處,其方程式考慮了狹義相對論中的時間延長效應(yīng)。這些方程式描述的是所觀察到的頻率的總差值,并具有相對論要求的洛侖茲對稱性。我們研究了狹義相對論的多普勒效應(yīng),并給出了廣義相對論的多普勒效應(yīng)的一般表達式。 在物理學(xué)中,當(dāng)觀測者在較弱引力場區(qū)域觀測時,來自較強引力場區(qū)域的光或者其它形式的輻射的波長會變長,這種效應(yīng)叫做引力紅移。相反地,當(dāng)觀測者在較強引力場區(qū)域觀測時,來自于較弱引力場區(qū)域的光或者其它形式的輻射的波長會變短,這種效應(yīng)叫做引力藍(lán)移。引力紅移和引力藍(lán)移統(tǒng)稱為引力頻移。本文研究了幾種引力場中的引力頻移現(xiàn)象：(1)在Schwarzschild引力場中,我們研究了其引力紅移,所得到的結(jié)果與對太陽的光譜頻率的觀測到的引力紅移一致；(2)在Reissner-Nordstrom引力場中,我們研究了電荷對頻移的影響,得到場源所含電荷對頻移的影響與電荷的正負(fù)無關(guān)；(3)在Kerr引力場中,我們討論了時空的角動量對頻移的影響,得到頻移效應(yīng)不僅與場源的質(zhì)量有關(guān),而且與時空的角動量有關(guān)；(4)在引力波時空中,其頻移是時間的函數(shù),而且頻移依賴于光信號在引力波場中的傳播方向。
[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.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：P131

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