The Doppler Effect In Curved Spacetime

Relativistic effects are important research areas in Astrophysics and Theoret-ical Physics. The researches on relativistic effects are important in understanding astronomical phenomena. This thesis focuses on the following two relastivistic ef-fects:(1)The Doppler effect,(2) the gravitational frequency shift (We call it the Doppler effect in curved spacetime)The relativistic Doppler effect is the change in frequency (and wavelength) of wave, caused by the relative motion of the source and the observer (as in the classical Doppler effect), taking into account the effects of special of relativity. The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity. The equations describe the total difference in observed frequencies and possess the required Lorentz symmetry. In this thesis, we investigate the relativistic Doppler effect and give the general expression of the relativistic Doppler effect.In physics, the wavelength of light or other forms of radiation originating from a region of strong gravitational field will be found to have a longer wavelength when received by an observer in a region of weak gravitational field. This effect is called the gravitational redshift. In contrary, the wavelength of light or other forms of radiation originating from a region of weak gravitational field will be found to be of a shorter wavelength when received by an observer in a region of strong gravitational field. This effect is called the gravitational blueshift. These two effects are collectively called gravitational frequency shift. In this thesis, we explore the gravitational frequency shift in several kinds of gravitational fields:(1) the Schwarzschild field spacetime. The expression for gravitational redshift obtained is in accurate agrement with the frequency shift of light from the sun.(2) in the Reissner-Nordstrom field spacetime, the effect of the charge on the frequency shifts is independent of the sign of the charge.(3) in the Kerr field spacetime, the frequency shift depends not only on the mass, but also on the angular momentum of the spacetime.(4) in the gravitational wave field spacetime, the frequency shift is a function of time, and depends on the propagation direction of the light signal with respect to the gravitational wave.