Editing Variable speed of light (section)

=== Background ===
Einstein's [[equivalence principle]], on which [[general relativity]] is founded, requires that in any local, freely falling reference frame, the speed of light is always the same.<ref>{{Cite book|last=Will|first=Clifford M.|author-link=Clifford Martin Will |url=https://books.google.com/books?id=gf1uDwAAQBAJ|title=Theory and Experiment in Gravitational Physics|date=2018-09-30|publisher=Cambridge University Press|isbn=978-1-108-57749-6|pages=238|language=en}}</ref><ref>{{Cite book|last1=Misner |first1=Charles W. |title=Gravitation |title-link=Gravitation (book) |last2=Thorne |first2=Kip S. |last3=Wheeler |first3=John Archibald |author-link1=Charles W. Misner |author-link2=Kip Thorne |author-link3=John Archibald Wheeler |date=2017-10-03 |publisher=Princeton University Press |isbn=978-1-4008-8909-9 |pages=297 |language=en}}</ref> This leaves open the possibility, however, that an inertial observer inferring the apparent speed of light in a distant region might calculate a different value. Spatial variation of the speed of light in a gravitational potential as measured against a distant observer's time reference is implicitly present in general relativity.<ref>{{cite book|first=S. |last=Weinberg|author-link=Steven Weinberg |url=https://archive.org/details/gravitationcosmo00stev_0|title=Gravitation and Cosmology|publisher=Wiley|year=1972|location=London|page=[https://archive.org/details/gravitationcosmo00stev_0/page/222 222]|isbn=9780471925675|url-access=registration}}</ref> The apparent speed of light will change in a gravity field and, in particular, go to zero at an event horizon as viewed by a distant observer.<ref>{{cite book|last1=Bergmann|first1=Peter|author-link=Peter Bergmann |title=The Riddle of Gravitation|url=https://archive.org/details/riddlegravitatio00berg_292|url-access=limited|date=1992|publisher=Dover|location=New York|isbn=978-0-486-27378-5|page=[https://archive.org/details/riddlegravitatio00berg_292/page/n116 94]|edition=1st reprint from 1968}}</ref> In deriving the [[gravitational redshift]] due to a spherically symmetric massive body, a radial speed of light ''dr''/''dt'' can be defined in [[Schwarzschild coordinates]], with ''t'' being the time recorded on a stationary clock at infinity. The result is
: <math> \frac{dr}{dt} = 1 - \frac{2m}{r}, </math>
where ''m'' is ''MG''/''c''<sup>2</sup> and where [[natural units]] are used such that ''c''<sub>0</sub> is equal to one.<ref>{{cite book|last1=Tolman|first1=Richard|author-link=Richard Tolman |title=Relativity Cosmology and Thermodynamics|date=1958|publisher=Oxford|location=Oxford UK|page=212|edition=1st reprint from 1934}}</ref><ref>{{Cite book |last=Stavrov |first=Iva |title=Curvature of Space and Time, with an Introduction to Geometric Analysis |title-link=Curvature of Space and Time, with an Introduction to Geometric Analysis |date=2020 |publisher=American Mathematical Society |isbn=978-1-4704-6313-7 |location=Providence, Rhode Island |oclc=1202475208 |page=179}}</ref>