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In physics, light loses energy when it moves away from a massive body such as a star or a black hole; this effect reveals itself as a 'gravitational redshift' in the frequency of the light, and is observable as a shift of spectral lines towards the longer, or "red," end of the spectrum.
Light moving into a region of stronger gravity shows a gravitational blueshift.

Contents

Definition

History

Important things to stress

Initial verification

Application

Exact Solutions

Gravitational Redshift vs. Gravitational Time Dilation

Primary sources

Links

Definition

Redshift is often denoted with the variable $z,$.

Where:
$lambda\_o,$ is the wavelength of the photon as measured by a distant observer.
$lambda\_e,$ is the wavelength of the photon when measured at the source of emission.
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:
$z\_\{approx\},$ is the displacement of spectral lines due to gravity as viewed by a far away observer in free space.
$G,$ is Newton's gravitational constant (the variable used by Einstein himself).
$M,$ is the mass of the body which the light is escaping.
$c,$ is the speed of light.
$r,$ is the radius of the star you consider.
Using the energy-momentum equation relating energy and wavelength of a photon, the gravitational redshift is equivalent to a loss of energy of the photon.

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). The effect of gravity on light was then explored by Laplace and Johann Georg von Soldner (1801) before Einstein rederived the idea from scratch in his 1911 paper on light and gravitation.
Einstein was accused by Philipp Lenard of plagiarism for not citing Soldner's earlier work - however, given that the idea had fallen so far into obscurity before Einstein resurrected it, it is entirely possible that Einstein was unaware of all previous work on the subject. In any case, Einstein went further and pointed out that a key consequence of gravitational shifts was gravitational time dilation. This was a genuinely new and revolutionary idea.

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. In other words, the observer must be standing "uphill" from the source.

★ Tests done by many universities continue to support the existence of gravitational redshift.

★ Gravitational redshift is not only predicted by general relativity. Other theories of gravitation support gravitational redshift, although their explanations for why it appears vary.

★ Gravitational redshift does not assume the Schwarzschild metric solution to Einstein's field equation - in which the variable $M;$ cannot represent the mass of any rotating or charged body.

Initial verification

Gravitational redshift was first observed in the spectral lines of the star Sirius B by Adams in 1925, although this measurement was criticized as possibly flawed, since it was difficult to rule out a shift of the spectral lines in the atmosphere of a white dwarf by some other (possibly unrecognized) effect.
The Pound-Rebka experiment of 1959 definitively measured the gravitational redshift in spectral lines. This was documented by scientists of the Lyman Laboratory of Physics at Harvard University.
More information can be seen at Tests of general relativity.

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:

ight)}}-1, 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 Redshift vs. Gravitational Time Dilation

When 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. Route-dependence due to frame-dragging may come into play, which would invalidate this idea and complicate the process of determining globally-agreed differences in underlying clock rate.
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.

Primary sources

Einstein, Albert. "Relativity : the Special and General Theory." Project Gutenberg.

Links

★ Tests of general relativity

★ Equivalence principle