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In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field. If applied to optical wave-lengths this manifests itself as a change in the colour of the light as the wavelength is shifted toward the red (making it: less energetic,longer in wavelength, and lower in frequency) part of the spectrum. This effect is called gravitational redshift and other spectral lines found in the light will also be shifted towards the longer wavelength, or "red," end of the spectrum. This shift can be observed along the entire electromagnetic spectrum.

Light that has passed "downhill" into a region of stronger gravity shows a corresponding increase in energy, and is said to be gravitationally blueshifted.

Contents 1 Definition 2 History 3 Important things to stress 4 Initial verification 5 Application 6 Exact Solutions 7 Gravitational Redshift vs. Gravitational Time Dilation 8 Primary sources 9 See also:

Redshift is often denoted with the variable .

Where:

is the wavelength of the electromagnetic radiation (photon) as measured by the observer. is the wavelength of the electromagnetic radiation (photon) when measured at the source of emission.

Gravitational redshift, the displacement of light towards the red, can (for the case of a star) 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:

is the displacement of spectral lines due to gravity as viewed by a far away observer in free space. is Newton's gravitational constant (the variable used by Einstein himself). is the mass of the body which the light is escaping. is the speed of light. 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.

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.

• 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. If the observer is at a lower gravitational potential than the source, a gravitational blueshift can be observed instead.

• Tests done by many universities continue to support the existence of gravitational redshift.^{[citation needed]}

• Gravitational redshift is not only predicted by general relativity. Other theories of gravitation support gravitational redshift, although their explanations for why it appears vary.^{[citation needed]}

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

A number of experimenters initially claimed to have identified the effect using astronomical measurements, and the effect was eventually considered to have been finally identified in the spectral lines of the star Sirius B by W.S. Adams in 1925. However, measurements of the effect before the 1960's have been critiqued by (e.g., by C.M. Will), and the effect is now considered to have been definitively verified by the experiments of Pound, Rebka and Snider between 1959 and 1965.

The Pound-Rebka experiment of 1959 measured the gravitational redshift in spectral lines using a terrestrial 57Fe gamma source. This was documented by scientists of the Lyman Laboratory of Physics at Harvard University. A commonly-cited experimental verification is the Pound-Snider experiment of 1965.

More information can be seen at Tests of general relativity.

Gravitational redshift is studied in many areas of astrophysical research.

A table of exact solutions of the Einstein field equations consists of the following:

	Non-rotating	Rotating
Uncharged	Schwarzschild	Kerr
Charged	Reissner-Nordström	Kerr-Newman

The more often used exact equation for gravitational redshift applies to the case outside of a non-rotating, uncharged mass which is spherically symmetric. The equation is:

, where

• is the gravitational constant,
• is the mass of the object creating the gravitational field,
• 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
• is the speed of light.

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.

• John Michell "On the means of discovering the distance, magnitude etc. of the fixed stars" Philosophical Transactions of the Royal Society (1784) 35-57, & Tab III

• Albert Einstein, "The effect of gravity on light" (1911)

• Albert Einstein, "Relativity: the Special and General Theory." (@Project Gutenberg).

• R.V. Pound and G.A. Rebka, Jr. "Gravitational Red-Shift in Nuclear Resonance" Phys. Rev. Lett. 3 439-441 (1959)

• R.V. Pound and J.L. Snider "Effect of gravity on gamma radiation" Phys. Rev. 140 B 788-803 (1965)

• R.V. Pound, "Weighing Photons" Classical and Quantum Gravity 17 2303-2311 (2000)

• Tests of general relativity
• Equivalence principle
• Gravitational time dilation
• redshift