What is a metric for uniformly moving frame?

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The discussion centers on the Schwarzschild Metric and its relationship to uniformly moving frames in special relativity (SR). It highlights that the Schwarzschild Metric, which accounts for gravitational effects, differs fundamentally from the Minkowski Metric used in SR, which describes flat spacetime without gravity. The time dilation factor in SR arises naturally from the metric, while in the Schwarzschild case, it incorporates both gravitational and kinematic effects. The conversation emphasizes that metrics can be expressed in different coordinates but fundamentally represent the same geometric object, regardless of the observer's motion. Ultimately, the Schwarzschild Metric and the Minkowski Metric serve different purposes in their respective contexts of general and special relativity.
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wil said:
This is obvious, because this setup is frame invariant, thus it must be simultaneity convention invariant also.
The mapping between B and events on O's worldline is neither frame invariant nor simultaneity convention invariant.

wil said:
In that setup we measure a local time duration between two real events, not between two abstract coordinates, which are not a real entities.
I have already shown that this is not true. Event B is not local to observer O.
 
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