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I'm very new to the concepts of SR/GR and curvature of spacetime.

My understanding is that the bending of spacetime is the causation of gravity, and that matter is the causation of the bending of spacetime. If this is the case, all matter bends spacetime to some degree. The more massive something is, the more spacetime will be bent and the more "gravity" will be experienced.

Could it then be said that, for example, if we stand near a massive (in the sense of containing lots of mass) building we will weigh more than if we did not (assuming weight as in the force)? Assuming and disregarding that the difference in weight could be almost negligible? If this is true, then I believe I can somewhat confirm my understanding of GR/SR.

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    $\begingroup$ This question is best discussed in the framework of Newtonian gravity, as the involved energy densities are small. And the answer is yes. You can even measure distortion of earth's gravity near a mountain! So if you see this effect in the Newtonian limit, of course it carries over to GR. $\endgroup$ – Sebastian Riese May 19 '15 at 21:13
  • $\begingroup$ When standing in a tunnel inside a mountain... You weigh less! Woaa! The word "weigh" needs a definition. $\endgroup$ – Steeven May 19 '15 at 22:54
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    $\begingroup$ Considering that the building's center of gravity is probably above our head the vertical component of its gravity force will be pointing upwards, so we will "weigh" less. With the building replaced by the Moon this is quite visibly "felt" by water during the tides. $\endgroup$ – Conifold May 19 '15 at 22:55
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First, as has been said in the comments, this has nothing to do with General Relativity per se and can be perfectly explained within Newtonian gravity.

The answer is yes, depending on what you mean by weight, since, after all, the building will pull you to the side. Weight is a force and forces are vectors; in this case, your weight will be longer and pointing a little bit to the side, but its vertical component will not change.

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