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