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cianfa72

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- Is acceleration absolute or relative - follow up: some doubts about static congruence and global coordinate chart for spacetime

Hello,

Some doubt arose me reading this thread https://www.physicsforums.com/threa...ute-or-relative-revisited.999420/post-6454462 currently closed. Sorry, I have not be able to quote directly from it

From my understanding in a

That does mean -- in the chosen global coordinate chart (frame) -- objects at rest (i.e. objects having worldlines described by fixed coordinate time) that move inertially actually have a

Some doubt arose me reading this thread https://www.physicsforums.com/threa...ute-or-relative-revisited.999420/post-6454462 currently closed. Sorry, I have not be able to quote directly from it

*Your claim is not , however, asserting that the spacetime geometry changes when you change coordinates. And the fact that the universe is "static" and the bucket is not can be expressed as invariant properties of the spacetime geometry and particular families of worldlines within it. For example (since this is an "I" level thread, some technical jargon is not inappropriate), the family of worldlines describing the motion of objects "at rest relative to the universe" will be integral curves of a timelike Killing vector field that is hypersurface orthogonal (which is what "static" translates to in more technical GR language); whereas the family of worldlines describing the motion of the bucket will be integral curves of a timelike Killing vector field (assuming the bucket's angular velocity of rotation relative to the universe is constant) that is not hypersurface orthogonal (in more technical jargon, the bucket's motion will be stationary but not static).*From my understanding in a

*static*spacetime there is*only one*'timelike Killing Vector Field (KVF) congruence' that is hypersurface orthogonal. There can be multiple "static" congruence of KVFs however they are actually*not*hypersurface orthogonal.*In a curved spacetime, such as the spacetime of our actual visible universe, there are no global inertial frames. The global frame we use to describe our universe is not inertial. Objects at rest in this frame are moving inertially (zero proper acceleration), but the frame as a whole is not inertial.*That does mean -- in the chosen global coordinate chart (frame) -- objects at rest (i.e. objects having worldlines described by fixed coordinate time) that move inertially actually have a

*not*null geodesic deviation though
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