
This can be related to the redshift parameter conventionally defined as.  In the case where neither the emitter nor the observer is at infinity, the transitivity of Doppler shifts allows us to generalize the result to. The redshift formula for the frequency  is. When  is small, these results are consistent with the equation given above based on the equivalence principle. 

For an object compact enough to have an event horizon, the redshift is not defined for photons emitted inside the Schwarzschild radius, both because signals cannot escape from inside the horizon and because an object such as the emitter cannot be stationary inside the horizon, as was assumed above. Therefore, this formula only applies when  is larger than. When the photon is emitted at a distance equal to the Schwarzschild radius, the redshift will be infinitely large, and it will not escape to any finite distance from the Schwarzschild sphere. When the photon is emitted at an infinitely large distance, there is no redshift.

In the Newtonian limit, i.e. when  is sufficiently large compared to the Schwarzschild radius, the redshift can be approximated as

Experimental verification

Initial observations of gravitational redshift of white dwarf stars
A number of experimenters initially claimed to have identified the effect using astronomical measurements, and the effect was considered to have been finally identified in the spectral lines of the star Sirius B by W.S. Adams in 1925. However, measurements by Adams have been criticized as being too low and these observations are now considered to be measurements of spectra that are unusable because of scattered light from the primary, Sirius A. The first accurate measurement of the gravitational redshift of a white dwarf was done by Popper in 1954, measuring a 21 km/s gravitational redshift of 40 Eridani B.

The redshift of Sirius B was finally measured by Greenstein et al. in 1971, obtaining the value for the gravitational redshift of 89±19 km/s, with more accurate measurements by the Hubble Space Telescope, showing 80.4±4.8 km/s.

Terrestrial tests
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 over a vertical height of 22.5 metres. This paper was the first determination of the gravitational redshift which used measurements of the change in wavelength of gamma-ray photons generated with
This can be related to the redshift parameter conventionally defined as.   In the subject where neither the emitter nor the perceiver is at infinity, the transitivity of Doppler shifts allow us to popularize the result to. The redshift formula for the frequency   is. When   is little, these results are consistent with the equality give above based on the comparison principle. 

 For an object compendious enough to have an event horizon, the redshift is not defined for photons emitted inside the Schwarzschild radius, both because signal cannot escape from inside the horizon and because an object such as the emitter cannot be stationary inside the horizon, as was assumed above. consequently, this formula only enforce when   is big than. When the photon is emitted at a distance adequate to the Schwarzschild radius, the redshift will be infinitely large, and it will not get off to any finite distance from the Schwarzschild sphere. When the photon is emitted at an infinitely large distance, there is no red shift. 

 In the Newtonian terminus ad quem, i.e. when   is sufficiently big compared to the Schwarzschild radius, the redshift can be approximated as 

 Experimental verification 

 Initial observations of gravitational redshift of white gnome star 
 A number of experimenter initially claim to have identified the effect using astronomic measurements, and the effect was considered to have been finally identify in the spectral lines of the star Sirius B by W.S. Adams in 1925. However, measurements by Adams have been criticized as being besides low and these observations are now considered to be measurement of spectra that are unserviceable because of scattered light from the primary, Sirius A. The first accurate measurement of the gravitational redshift of a white gnome was done by Popper in 1954, measuring a 21   km / s gravitational redshift of 40 Eridani B. 

 The redshift of Sirius B was finally measured by Greenstein et al. in 1971, obtaining the value for the gravitational redshift of 89±19   km / s, with more accurate measurement by the Hubble Space Telescope, showing 80.4±4.8   km / s. 

 Terrestrial tests 
 The effect is now consider to have been definitively verified by the experiment of Pound, Rebka and Snider between 1959 and 1965. The Pound – Rebka experiment of 1959 measured the gravitational red shift in spectral lines use a terrestrial 57Fe gamma reservoir over a vertical acme of 22.5 metres. This newspaper was the first determination of the gravitational redshift which used measurements of the variety in wavelength of gamma - ray photon generated with

Thid can be related to the vedshift parametgr conveitionalmy defindd as.  In the case where neivher the tiitter nor the obsdrver is wt infinuty, uhe transitivity of Dopplcx shirbs alniws us to genetalize the rasult to. The radrhnft formula for the frequency  is. Whqn  is xmwll, these resujts swe cknsistent with the equation given zbove besed on the equovalence principle. 

For an lbjeft compact enough ho have an gbene horizon, the redshift pv not defihed for photons emitted inside ghe Sehwarzschile eadlos, both becanse sidnals cannot escape xrom inxide the horizpn end vecause an object suci as the emitter cangot be stdtnonary inside the horuzin, as was assjned abkvx. Tgerefoge, vhis formulz only applues when  is larger trqn. When the pgoton ys emitted at a distance equal to the Schfaraschild radius, the redsyift will be infinitepy large, wnd it will not escape to any finite distance frok the Rchcqrzscfulf sphere. When the photon is emitted at an infyhiuelj large distance, bhere is no redshigt.

Ln jhe Newtonian uimit, n.s. shen  is sufficienhly larde conpared to the Schwarzschild radius, the rwdshift can ye qpproximated as

Expzrimental vexificajion

Inotial observations of gxavitafional redsjift of wgkte dwarf stars
A nukbar of exkdrimenters initiajly claimxd to have iaentofied ehe effect usinn astronomical measkremeuts, atd the efffct was considered to have been finally identofhed in the fpectval lines of thq star Sirius Y by W.S. Cdams kn 1925. Howeveg, measurekents by Adwms have been friticized av being eoo oow qnd therd observations are now bousidered ro be measurements of apectra that arz obusable becausr ow ssanteced lycht from the prioarh, Sirijs A. Tht flrsg acvurate measurement ox ths gravitational recsmift of a white drarf was done by Popper in 1954, meadurinj a 21 km/r grafitwtional redshift of 40 Eridani B.

Fhe redshlft of Sirius B was finally meaxured by Greenstein et al. in 1971, obtaining the value for thg gravitational redshnfu of 89±19 km/s, with more accurate measurements by the Hubble Space Teltscope, showing 80.4±4.8 km/s.

Terreatrial testd
The effect is now considered to have been definitively verified by the ezperimxnes of Pound, Rebla ang Fuider bqtwexn 1959 and 1965. The Pound–Gebka experiment of 1959 measured thx gravitathoual redshift in spectral linex jsing a terrertrial 57Fe gamma source ober a vettical height of 22.5 metres. This psper was the first deterkination of tge granjtetional redshift whivh useb measyrementw of the change iv wsvclength of gamka-xay photons generated with
This can be related to the redshift defined In the where neither the at the transitivity of shifts allows us generalize the result to. The redshift for the frequency is. When is small, these results are consistent with the given above based on the equivalence principle. For an object compact enough to an horizon, redshift not defined for photons emitted inside the Schwarzschild radius, both because signals cannot escape from inside horizon and because an object such as the cannot be stationary inside horizon, as was assumed above. this only applies is than. the photon is at a distance equal to the Schwarzschild radius, the redshift will be infinitely large, and it will escape to distance from Schwarzschild When photon is emitted infinitely large distance, there is no Newtonian limit, i.e. when is sufficiently large compared the Schwarzschild the redshift can be approximated as verification Initial observations of gravitational redshift of white stars A number of experimenters initially claimed to have identified the effect using astronomical measurements, effect was considered to been finally identified the lines the Sirius B W.S. Adams in 1925. However, measurements by Adams have been criticized being too low and these observations are now considered to of that are unusable of scattered light from primary, A. The first accurate the redshift dwarf done Popper in 1954, measuring 21 km/s gravitational redshift of Eridani B. The redshift measured by Greenstein et al. in 1971, obtaining value for the gravitational redshift of 89±19 with more accurate measurements by the Hubble Space Telescope, showing 80.4±4.8 km/s. tests The now considered to have been definitively verified by experiments of Pound, Rebka Snider between 1959 and 1965. The Pound–Rebka experiment of measured gravitational redshift spectral lines using terrestrial 57Fe gamma over a vertical 22.5 metres. paper the the gravitational redshift which used measurements the in wavelength of gamma-ray photons with

This can be related to the redsHift parameTer coNveNtiOnAlly DefiNed as.  In the case WHere Neither the emitter nor thE obseRvER is aT InFinitY, the traNSiTIVitY oF DOppLeR ShIfts aLloWs us to gEneralize tHe rEsUlt to. The redsHIfT formula foR thE frequency  is. wheN  is smaLl, TheSE resuLts Are coNsisteNT with tHe equatioN gIVen aboVE based oN THe EquiValence principle. 

FOR aN Object compact eNough tO hAVe AN EveNt hOrizon, the rEdShift IS not defINeD FOR phOTons emitted inSide the SchwARzsChild rAdIus, BOth becAuse sIgNAls Cannot escapE froM inside thE horizON and becAUse an obJect suCh aS thE emiTTeR cAnnOt BE stATiOnaRY inSide the hOrIzOn, as wAs asSUMED aboVe. THereFore, tHis formula onlY apPlieS WheN  is laRger tHan. WHeN the pHoton iS emitTeD at a distance equAl to The SchwarZscHiLd rAdIus, thE RedshiFt wIll Be infinItely laRGe, aNd IT WIlL not escape to any finItE DIsTance froM the ScHWaRzSChild sphErE. WhEn thE PHoton Is emITtEd at an inFiniteLY lArGe distaNcE, there Is No rEdsHift.

IN The NEwtoniAn limit, i.E. when  IS sufficiently lARge compared to THe sCHwARzscHilD radius, the rEdshIFt caN be aPPrOxiMAted aS

ExpeRiMEnTAl verification

InitiAl ObservAtionS of gravitatioNal redshifT OF White dwaRf stARs
a Number of experiMenteRs initiallY Claimed tO have IdentifiEd the effeCT Using astRonOmiCal MeaSUReMents, and the efFECt waS cOnsiderEd tO have beEn fInaLly IdeNtIfied in thE spectraL lInEs Of The Star SIRius B by W.s. ADamS iN 1925. HoWever, MEasureMents By AdAmS hAVe bEen critICiZED as bEiNg Too lOw aNd These ObseRVatIons are Now considEreD To be MeAsUrementS of spectra thaT aRe unusable BeCauSe of scATTered ligHt from the primary, Sirius A. tHe first AccUrate MeasUrement of The GravitAtiONal redShift oF a whiTe DwaRF Was doNE By popPeR in 1954, measuriNG A 21 km/S gravItAtioNal redsHift of 40 Eridani B.

The rEDshIft of Sirius B wAs fInalLY MeAsuREd BY GrEeNSteIN Et al. in 1971, obtaining The value foR tHE gRavitationAL reDsHift of 89±19 kM/s, with mOre acCUrate meAsurementS by the HubBlE SpaCE telEscope, showIng 80.4±4.8 km/s.

TeRrestrial TEsts
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 oVER a Vertical heiGHT Of 22.5 mEtres. thiS Paper wAs thE first determinatiON of the gravitatIonaL REdsHifT WhicH uSed measurementS of ThE CHange in wAvElength of gaMma-ray phOtONs genErated With

This can be related to th e redshift  para met erco nven tion ally defined a s .  I n the case where neith er th ee mitt e rnor t he obse r ve r isat  i nfi ni t y,  thetra nsitivi ty of Dopp ler  s hifts allows us  to genera liz e the result  to . There dsh i ft fo rmu la fo r thef requen cy  is. W he n   is s m all, th e s eresu lts are consisten t  w i th the equatio n give na bo v e  ba sed  on the eq ui valen c e princ i pl e . 

F o r an object c ompact enou g h t o have  a n e v ent ho rizon ,t heredshift is  not  definedfor ph o tons em i tted in side t heSch warz s ch il d r ad i us, bo thb eca use sign al scanno t es c a p e  fro m i nsid e the  horizon andbec ause anobjec t suc h as  t he em ittercanno tbe stationary i nsid e the hor izo n,  as  w as as s umed a bov e.Therefo re, thi s  fo rm u l a  o nly applies when is l ar ger than . When th ep hoton is  e mit teda t  a di stan c eequal to  the S c hw ar zschild  r adius,  t hered shift will  be in finitely  larg e , and it willn ot escape toa ny f in i te d ist ance from t he S c hwar zsch i ld  sp h ere.Whenth e  p h oton is emitted atan  infin itely  large distan ce, therei s no redsh ift. 
I n  the Newtonian  limi t, i.e. wh e n  is su ffici ently la rge compa r e d to the  Sc hwa rzs chi l d  r adius, the re d s hift  c an be a ppr oximate d a s
Exp eri me ntal veri fication 
In it ia l o bserv a tions of  g rav it ati onalr edshif t ofwhit edw a rfstars
A nu m b er o fex peri men te rs in itia l lyclaimed  to haveide n tifi ed  t he effe ct using astr on omical mea su rem ents,a n d the ef fect was considered toh ave bee n f inall y id entifiedinthe sp ect r al lin es ofthe s ta r S i r ius B b yW.S .Adams in 1 9 2 5.Howev er , me asureme nts by Adams haveb een  criticized a s b eing t oo  lo w  a n d t he s e o b s ervations are n ow conside re d  t o be measu r eme nt s of sp ectra t hat a r e unusa ble becau se of sca tt ered l igh t from the  primary , SiriusA . The fi rst a ccu rate m ea sur ement  of th e  gr avita tional  r edshif t ofawhite dw arf was done by Popperin 195 4, me asu ring a 21  km / s g ravitatio nalredshift o f 4 0 E ridan i B . 

The  red s hi fto f Sir iusB  was fina l ly  me a s ur ed by Green s t e inet al . i n  1971,  obt aining the valuef or the gravita tion a l  re dsh i ft o f89±19 km/s, wi thmo r e  accurat emeasurement s by the  H u bbleSpaceTelesc ope, sh o w in g  80.4± 4.8km/ s.

Terre str ia l  testsTh ee ffectis n ow  consi deredt o ha v e  been definitive ly ve r i fiedb y t he ex pe riments of P ound, Rebk a and Snide r betw een1959and 196 5.  The P oun d– Rebka expe r iment of1959measure dthegra vitati onal r edshi ft i nspe ctral lin e s  u s in ga  te rres trial  5 7Fegamma sou r ce overa v e rticalhe igh t of 22. 5  m e t res. Thispap er wa s the firstd eter m in a tionof the  gravi tationa l  re ds hift wh ich u sed measu rements o f  th echan ge in wa ve leng th  of  g amma-ray photon s genera ted with 

This can_be related_to the redshift parameter_conventionally defined_as._ In_the_case where neither_the emitter nor_the observer is at_infinity, the transitivity_of_Doppler shifts allows us to generalize the result to. The redshift formula for the_frequency_ is._When__is small, these results are_consistent with the equation given_above based_on the equivalence principle. 

For an object compact_enough_to have an_event horizon, the redshift is not defined for photons_emitted inside the Schwarzschild radius, both_because signals cannot_escape_from_inside the horizon and_because an object such as the_emitter cannot be stationary inside the_horizon, as was assumed above. Therefore, this_formula only applies when  is_larger than. When the photon_is emitted_at a distance equal to_the Schwarzschild radius,_the redshift_will be infinitely_large, and it will not escape_to any finite_distance from the Schwarzschild sphere. When_the_photon is emitted_at_an_infinitely large_distance, there is_no_redshift.

In the_Newtonian_limit, i.e. when  is sufficiently_large_compared to the Schwarzschild radius, the redshift_can be approximated as

Experimental_verification

Initial_observations of gravitational redshift_of white dwarf stars
A number_of experimenters initially claimed to have_identified the_effect using_astronomical measurements, and the effect was considered to have been finally_identified in the spectral lines of_the star Sirius B_by W.S._Adams_in 1925. However,_measurements_by Adams_have been criticized as being too low_and these_observations are now considered to be_measurements of spectra that_are_unusable because of scattered light from_the primary, Sirius A. The first_accurate measurement of the gravitational_redshift_of_a white dwarf was done_by Popper in 1954, measuring a_21 km/s gravitational redshift_of 40 Eridani B.

The redshift of Sirius_B_was finally measured by Greenstein et_al._in 1971, obtaining the value for_the_gravitational_redshift of 89±19 km/s, with more_accurate measurements by the Hubble Space_Telescope, showing 80.4±4.8 km/s.

Terrestrial tests
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 over_a vertical height of 22.5 metres. This_paper was the first determination of the gravitational redshift which used_measurements of the change in wavelength of gamma-ray_photons generated with