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precession-of-Mercury vs 3-geometries: vocabulary for the difference?

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[If the answer to the question below is "no", then this post might be viewed as provocative. Sorry! But if the answer is "yes", then this post will have been a good thing. Only one way to find out.]

A member of the GR cognoscenti recently told me that, if f is a diffeomorphism, then f_* is routinely called the "push-forward" operation (on tensor fields). This bit of vocabulary has been a blessing. I'm now seeking a similar blessing. Here are two observables:

A. The precession of the orbit of Mercury is an observable that we compute with the help of classical GR. This observable is defined only in our particular state of reality.

B. If we (somehow) foliate spacetime into 3-geometries at differing times, then the (rather complicated) value of the 3-geometry at time t can be observed in any state.

It seems to me that A and B come from qualitatively different classes of observables. Are there routine names for these?

This post has been migrated from (A51.SE)

asked Apr 12, 2012 in Theoretical Physics by Greg Weeks (50 points) [ no revision ]

First, I don't understand what is asked here. Second, if it is general physics (i.e. not research-level) http://physics.stackexchange.com/ is a more suitable site.

This post has been migrated from (A51.SE)

commented Apr 12, 2012 by Piotr Migdal (1,260 points) [ no revision ]

Research-level is when it is related to current, mainstream research. However, what is even more important is if it is is clear, objective and answerable (see [FAQ](http://theoreticalphysics.stackexchange.com/faq)).

This post has been migrated from (A51.SE)

commented Apr 12, 2012 by Piotr Migdal (1,260 points) [ no revision ]

Boy do I feel foolish. The distinction that I was making was silly, and I won't waste anyone's time by describing my confusion. (A confusion that I had for about thirty years. Yeesh.) Thanks for not buying it.

This post has been migrated from (A51.SE)

commented Apr 14, 2012 by Greg Weeks (50 points) [ no revision ]

Here you may find a simple post-Newtonian solution for Mercury's orbit precession
Gravity is a little big bigger than in Newton’s law; it increases with speed -kinetic energy- where the maximum is the double gravity in the case of light.
Global Physics also predicts the anomalous precession of Mercury’s orbit as Paul Gerber did 20 years before Einstein. https://molwick.com/en/gravitation/077-mercury-orbit.html

commented Sep 19, 2017 by Jose [ no revision ]

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