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As seen from outside the gravitational field of an object (a black hole, say) in (where the field is very weak) clocks inside the field are observed to run at a slower pace, the length of measuring rods to look shorter nearer to its source as the field is stronger compared to the field at the observer. Does this mean that the rest energy of the object just warps an already existing spacetime (which exists even in the absence of the object) or is the field itself to some extent a local extension of spacetime -in which case the creation of energy would be the creation of spacetime?

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  • $\begingroup$ What do you mean by "its gravitational field"? $\endgroup$
    – user76284
    Jun 22, 2020 at 22:18
  • $\begingroup$ It's perfectly valid to describe spacetime in the absence of curvature. $\endgroup$
    – Charlie
    Jun 22, 2020 at 23:05
  • $\begingroup$ Well, as space and time don’t exist, as the length of the meter and duration of the second aren’t defined in a universe devoid of energy* -of curvature- then you can calculate what you want but is doesn’t then refer to anything real. * Ignoring that there cannot exist a universe devoid of energy. $\endgroup$
    – Anton
    Jun 22, 2020 at 23:15
  • $\begingroup$ Not sure I follow - gravity is spacetime curvature. I've read your question through a few times but I don't quite see what you're asking. $\endgroup$ Jun 22, 2020 at 23:25
  • $\begingroup$ Is the gravitational field -which is an area of curved spacetime- just a volume of spacetime which would exist even in the absence of the object, a spacetime which just is warped, deformed in the environment of the object by its presence, or is its field nearer to its mass center also, to some extent, a local extension of spacetime? Is the distance between the observer and the mass center of the object (not a black hole) as measured inside the field greater than as measured outside of it, as inferred from the positions of the observer and the center of the object relative to surrounding stars? $\endgroup$
    – Anton
    Jun 22, 2020 at 23:41

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The Einstein equations answer your question, the curvature of the space time is related to the mass, which is related to the energy. The concept of gravitational field is one from Newtonian mechanics, and is replaced by curvature of spacetime in General Relativity.

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