Does time dilation cause redshift?

d0wnl0w
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This may be an easy answer for AtsroPhys vetrans. But I'm assuming since the doppler effect of an accelerating galaxy causes reshift, then the time dilation from a gravitational field would do the same. This is referring to very powerful fields, and also to redshift in all waves (not just visible light).
 
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Thanks.. For some reason I couldn't find it when I searched.
 

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