| [ home ] | Gravitaional redshift. Gravitational waves. | General Relativity. Note: « 12 » |
In a weak gravitational field the space−time is almost flat and the metric tensor gab is equal to the flat metric ηab plus a small correction hab, gab = ηab+hab. The Riemann tensor to the lowest order in hab is
The intensity of gravitational radiation by a system of slowly moving bodies is determined by its quadrupole moment Dαβ
Gravitational red shift is a change of the frequency of the electro−magnetic radiation as it passes through a gravitational field. It is a direct consequence of the equivalence principle. Gravitational red shift is one of the classical tests of general relativity (the others being Mercury perihelion advance and light bending).
The connection between the proper time interval Δτ and the world time interval Δt (here we only consider stationary gravitational fields where such world time can be introduced) is Δτ = √[g00]Δt.
Since frequencies are inversely proportional to the time intervals the corresponding connection between world frequency ω0 and the locally measured frequency ω is ω = ω0/√[g00] . In a weak gravitational field g00=1+2φ and therefore ω = ω0(1 − φ). A photon emitted from a point with φ1 and received at a point with φ2 will be shifted by Δω = (φ1−φ2)ω.
Experimental verification of the gravitational redshift requires good clocks since at Earth the effect is small. The first experimental confirmation came as late as in 1959, in the Pound−Rebka experiment [R.V. Pound and G.A. Rebka, Apparent weight of photons, Phys. Rev. Lett. 4, 337 (1960)] later improved by Pound and Snider. The famous experiment is generally called the Pound−Rebka−Snider experiment. They used Mossbauer effect to accurately meauser the change of frequency of a photon travelling upwards 22 m in the Earth's field.