Testing the Equivalence Principle with Spectral Anisotropies

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HarryWertM
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It suddenly occurred to me that I've never heard of a test of the Equivalence Principle itself - such as something like ...

An accelerating laboratory [in space] can see very obvious effects in external astronomical observations. Depending on the rate of acceleration, there would be 'forward / backward' anisotropies in the galactic field spectra well as the CMB spectrum. If you 'hovered' over our moon, say, or 'hung' from a lunar tether at L1, would it be possible to detect spectral anisotropies looking away / towards the local gravitational field?
 
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I guess what I really meant to ask is what would GR predict as the result for the experiment I describe. Some related questions:

1. Is there a spectral shift in images of objects observed in gravitational lensing?

2. Can you [in theory] produce a 'lensing' effect, the same as gravitation, with acceleration?