A frequency shifting of light to lower frequencies for sources emitting light in a relatively strong gravitational field; also called the Einstein shift. It means that light travelling away from a massive body appears at a lower frequency (redshifted) than expected. The redshift of light travelling away from Earth was first measured in 1961 by Robert Pound and Glen Rebka using the Mössbauer effect. Interpreted as the faster running of clocks in regions of weaker gravitational fields, it was demonstrated by comparing atomic clocks flown at high altitude (lower gravitational field) with clocks left on the ground (higher gravitational field); the high altitude clocks ran more quickly. Considered by Einstein a test of general relativity, the effect is now viewed as a test of the equivalence principle.
Light coming from a region of weaker gravity shows a gravitational blueshift.
Definition
Gravitational redshift is often denoted as the variable z.
Where:
λo is the wavelength of the photon as measured by a distant observer.
Gravitational redshift, the displacement of light towards the red, can be predicted using the formula provided in the theory of General Relativity (Albert Einstein: Relativity - Appendix - Appendix III - The Experimental Confirmation of the General Theory of Relativity):
Where:
zapprox is the displacement of spectral lines due to gravity as viewed by a far away observer in free space.
History
The gravitational weakening of light from high-gravity stars was predicted by John Michell in 1783, using Isaac Newton's concept of light as being composed of ballistic light corpuscles (see: emission theory). In any case, Einstein went further and pointed out that a key consequence of gravitational shifts was gravitational time dilation.
Important things to stress
The receiving end of the light transmission must be located at a higher gravitational potential in order for gravitational redshift to be observed.Initial verification
The Pound-Rebka experiment of 1969 demonstrated the existence of gravitational redshift in spectral lines.
Application
Gravitational redshift is studied in many areas of astrophysical research.
Exact Solutions
A table of exact solutions for gravitational redshift consists of the following:
| Non-rotating | Rotating | |
| Uncharged | Schwarzschild | Kerr |
| Charged | Reissner-Nordström | Kerr-Newman |
The more often used exact solution is for gravitational redshift of non-rotating, uncharged masses which are spherically symmetric. The equation for this is:
, where
G is the gravitational constant, M is the mass of the object creating the gravitational field, r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), and c is the speed of light. Gravitational Time DilationWhen using special relativity's relativistic Doppler relationships to calculate the change in energy and frequency (assuming no complicating route-dependent effects such as those caused by the frame-dragging of rotating black holes), then the Gravitational redshift and blueshift frequency ratios are the inverse of each other, suggesting that the "seen" frequency-change corresponds to the actual difference in underlying clockrate.
While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account.
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