GRAVITATIONAL REDSHIFT FULL

It turns out that just like for sound waves, the wavelength of light emitted by an object that is moving away from you is longer when you measure it than it is when measured in the rest frame of the emitting object. The Doppler effect can happen for light waves too (though it can't be properly understood without knowing special relativity). You've experienced the Doppler effect if you've ever had a train go past you and heard the whistle go to a lower pitch (corresponding to a longer wavelength for the sound wave) as the train moves away. In fact, only in the first case (a nearby body moving away from the earth) is the redshift caused by the Doppler effect. But there's a subtle difference, which you sort of allude to. its wavelength will be stretched, so the color of the light is more towards the red end of the spectrum.

In both cases, the light emitted by one body and received by the other will be 'redshifted' - i.e. The extent to which this result is a manifestation of the strong equivalence principle, satisfied, as far is known, only by general relativity, is also noted.If a body was launched from earth reaching a high constant velocity away from earth, in what way would the Doppler effect between earth and that departing body be any different than any Doppler effect between the earth and a distant body moving away from earth at the same velocity due only to the expansion of space? To this layman, it seems that in the case of the body launched from earth, the Doppler effect results from the waves having to deal with the rapid and constant increase in the units of space between the two bodies (not to the expansion of those units of space separating them) while in the case of the distant body, any Doppler effect would be affected by the expansion of the units of space through which those waves were traveling (not to the addition of units of space between them). The significance of this conclusion for the binary pulsar PSR 1913 + 16, where the gravitational redshift of the pulsar's frequency caused by the gravitational field of its companion is an observable effect, is discussed. The result is independent of how relativistic the clock may be. For an observer at infinity, the redshift Z ≡ Δv v is given by Z = −Gm Rc 2, where m is the mass of the distant object and R its distance from the clock in question. In all three cases the redshift is the same as if the clocks were non-gravitational, thereby governed by the Einstein equivalence principle. Three specific examples are treated: (i) the redshift of the angular frequency of a rotating relativistic star in the gravitational field of a distant body (ii) the redshift of the angular velocity of a slowly rotating black hole surrounded by an axisymmetric ring of matter and (iii) the redshift of the observed orbital period of a nearly circular, post-Newtonian binary system in the field of a distant, third body.

GRAVITATIONAL REDSHIFT FULL

Because the clocks in question have structure and dynamics determined by gravitational interactions, the full machinery of Einstein's equations must be used.

The gravitational redshift of gravitational clocks in a given weak gravitational field, within general relativity, is considered.

Gravitational redshift