Editing Redshift (section)

===Gravitational redshift===
{{Main|Gravitational redshift}}
In the theory of [[general relativity]], there is time dilation within a gravitational well. Light emitted within the well will appear to have fewer cycles per second when measured outside of the well, due to differences in the two clocks.<ref>{{Cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1st |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|284}}  This is known as the [[gravitational redshift]] or ''Einstein Shift''.<ref>{{cite journal | last=Chant | first=C. A. | bibcode = 1930JRASC..24..390C | title = Notes and Queries (Telescopes and Observatory Equipment – The Einstein Shift of Solar Lines) | date = 1930 | journal = [[Journal of the Royal Astronomical Society of Canada]] | volume = 24 | page = 390 }}</ref> The theoretical derivation of this effect follows from the [[Schwarzschild solution]] of the [[Einstein field equations|Einstein equations]] which yields the following formula for redshift associated with a photon traveling in the [[gravitational field]] of an [[Electric charge|uncharged]], [[rotation|nonrotating]], [[spherical symmetry|spherically symmetric]] mass:

:<math>1+z=\frac{1}{\sqrt{1-\frac{2GM}{rc^2}}},</math>

where
* {{math|''G''}} is the [[gravitational constant]],
* {{math|''M''}} is the [[mass]] of the object creating the gravitational field,
* {{math|''r''}} is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a [[Schwarzschild coordinates|Schwarzschild coordinate]]), and
* {{math|''c''}} is the [[speed of light]].

This gravitational redshift result can be derived from the assumptions of [[special relativity]] and the [[equivalence principle]]; the full theory of general relativity is not required.<ref>{{cite journal | last = Einstein | first = A. | author-link = Albert Einstein | date = 1907 | title = Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen | journal = Jahrbuch der Radioaktivität und Elektronik | volume = 4 | pages = 411–462 | bibcode=1908JRE.....4..411E}} See p. 458 ''The influence of a gravitational field on clocks''</ref>

The effect is very small but measurable on Earth using the [[Mössbauer effect]] and was first observed in the [[Pound–Rebka experiment]].<ref>{{cite journal | doi = 10.1103/PhysRevLett.4.337 | title = Apparent Weight of Photons | date = 1960 | last1 = Pound | first1 = R. | last2 = Rebka | first2 = G. | journal = Physical Review Letters | volume = 4 | issue = 7 | pages = 337–341 | bibcode=1960PhRvL...4..337P| doi-access = free }}. This paper was the first measurement.</ref> However, it is significant near a [[black hole]], and as an object approaches the [[event horizon]] the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the [[cosmic microwave background]] radiation (see [[Sachs–Wolfe effect]]).<ref>{{cite journal | last1=Sachs | first1=R. K. | author-link=Rainer K. Sachs | last2=Wolfe | first2=A. M. | author-link2=Arthur M. Wolfe | date=1967 | title=Perturbations of a cosmological model and angular variations of the cosmic microwave background | journal=Astrophysical Journal | volume=147 | issue=73 | doi=10.1086/148982 | page=73 | bibcode=1967ApJ...147...73S }}</ref>