Gravitational Red Shift

According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source could also be produced by the appropriate gravitational field. Thus the expected shift in radiation frequency in a gravitational field can be related to the relativistic doppler shift experienced from an accelerating light source.
 
source http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html