Why are gravity forces on going in the context of GR

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I am new to General Relativity, so please excuse my ignorance ahead of time. :)

While attempting to grasp the concept of bending spacetime I was stumped by the concept of continual gravitational forces and how they exist in the concept of GR. To clarify I understand the following as reasonable to say, that given the bending of spacetime the moon orbits about the earth not because it is actually rotating about, but rather because the definition of the straight line path that the moon was taking has been redefined due to a bending of spacetime by the earth. However where I am having trouble is the concept of a book on a table. Gravity is not pushing on the book downward but rather the table is pushing up on the book due to the books original path of travel being redefined to point to the center of the earth (the table is just in the way). Sounds good, however why is the force continual. Meaning why does the book not decelerate by the table and then float off, to illustrate, if I threw the book at the wall in a straight line it would hit the wall and then bounce, not stick to it and stay there with a force based on its weight. To follow that same point if there is no motion of either body in the depths of space would the two attract? Given Newton the answer is yes, however with neither body moving irregardless of straight line definitions it would seem (by my limited understanding) that with GR the answer would be no. Again sorry for the lame question, however I am really stumped by this.

By the way I am currently reading Spacetime and Geometry (Carroll) and using Gravity (Hartle) as a reference. If you have recommendations for any GR books I would be interested.

Thanks
 

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  • #2
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At each point in time (and the position of the book, and zero velocity in the earth frame), the corresponding geodesic leads to the center of earth. The force of the table constantly pushes the book "away" from those geodesics "into" other ones.

To follow that same point if there is no motion of either body in the depths of space would the two attract?
Yes.

GR is not a curved space, it is a curved spacetime, and the time-like components can give you geodesics like this.
 
  • #3
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As mfb explained, it's curved space-time that's relevant in GR. An object at rest takes a straight path through space-time, since they must move forward through time. Other inertial frames of reference differ in the angle of this line, but they always travel in straight lines through space-time. However, accelerating observers take curved trajectories through 4 dimensional space-time. Since massive bodies warp space-time, objects at rest try to follow geodesics, but since space-time is curved, this amounts to taking a curved trajectory. So, an object at rest in a gravitational field accelerates towards the center of mass.
 
  • #4
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I am new to General Relativity, so please excuse my ignorance ahead of time. :)

While attempting to grasp the concept of bending spacetime I was stumped by the concept of continual gravitational forces and how they exist in the concept of GR. To clarify I understand the following as reasonable to say, that given the bending of spacetime the moon orbits about the earth not because it is actually rotating about, but rather because the definition of the straight line path that the moon was taking has been redefined due to a bending of spacetime by the earth. However where I am having trouble is the concept of a book on a table. Gravity is not pushing on the book downward but rather the table is pushing up on the book due to the books original path of travel being redefined to point to the center of the earth (the table is just in the way). Sounds good, however why is the force continual. Meaning why does the book not decelerate by the table and then float off, to illustrate, if I threw the book at the wall in a straight line it would hit the wall and then bounce, not stick to it and stay there with a force based on its weight. To follow that same point if there is no motion of either body in the depths of space would the two attract? Given Newton the answer is yes, however with neither body moving irregardless of straight line definitions it would seem (by my limited understanding) that with GR the answer would be no. Again sorry for the lame question, however I am really stumped by this.

By the way I am currently reading Spacetime and Geometry (Carroll) and using Gravity (Hartle) as a reference. If you have recommendations for any GR books I would be interested.

Thanks
With the book sitting on the table, it is hard to imagine how it can be accelerating upward. Why doesn't one see it rising upward? The situation is really similar to what you have with centrifugal acceleration. Have you ever gone on the Roundup ride at an amusement park, where the platform is rotating around an axis, and where they then drop the bottom out, and you are pinned against the rim. There is a force acting on you by the rim, but you don't move radially inward toward the center of rotation. In the GR situation, the time direction and the radial direction are participating in the rotation.

Chet
 

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