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That doesn't seem to be what's going on in this thought experiment, as it's not using GR.

But while we are on the topic I'm curious if the physics you describe make it possible to build a perpetuum mobile.

GC used in GR implies conservation of energy due to the GL4 symmetry with respect to the time dimension in its differentiable geometry along with Noether's theorem. A breakage of GR on the cosmic scale might be with the super oscillatory phenomenon appearing around an isolated and fairly inactive dark star ("black hole") when a star passes in line behind it and the corresponding frequency bump in the spectrum as light is "mirrored" or trapped around the dark star is observed. Systems that do not adhere to the requirements of the FT could show perpetual motion while the causality proposition seems less likely to find violations, although a duality is "rough"ly around those two.

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