- #1

ORF

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Does the spacetime curvature produced by an object affect the object itself?

Thank you in advance :)

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In summary: I interpret "an object" to be not the same as a point-particle. Perhaps the spirit of the OP is to treat them the... same way?

- #1

ORF

- 170

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Does the spacetime curvature produced by an object affect the object itself?

Thank you in advance :)

Greetings!

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- #2

PAllen

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- #3

WannabeNewton

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ORF said:Does the spacetime curvature produced by an object affect the object itself?

Yes; this is due to the gravitational self-force mechanism. See: http://arxiv.org/pdf/0907.0412v1.pdf

- #4

Mueiz

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different parts of a body on other part ..but a single object can not affected by itself .this can by understood directly from the Principle of Equivalence because the motion of an object in gravitational field does not affected by the mass of the body and thus the curvature produced by it.

- #5

PAllen

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The principle equivalence is exact only in various limits. The source WBN cites quantifies the degree to which bodies deviate from exact geodesic motion due to self gravity.Mueiz said:

different parts of a body on other part ..but a single object can not affected by itself .this can by understood directly from the Principle of Equivalence because the motion of an object in gravitational field does not affected by the mass of the body and thus the curvature produced by it.

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- #6

1977ub

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ORF said:

Does the spacetime curvature produced by an object affect the object itself?

Thank you in advance :)

Greetings!

An extended object would consist of an ensemble of interacting particles. Presumably part of this interaction would consist of spacetime distortions aka "gravitational forces" ?

- #7

PeterDonis

Mentor

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1977ub said:An extended object would consist of an ensemble of interacting particles. Presumably part of this interaction would consist of spacetime distortions aka "gravitational forces" ?

Not quite. In GR, gravity is not an "interaction"; it's just spacetime geometry. But the spacetime geometry determines which worldlines are geodesics, i.e., which particle trajectories are freely falling. Interactions between particles will cause at least some of them to move on worldlines which are not freely falling, but exactly which worldlines the particles end up following will depend on a combination of the interactions and the underlying spacetime geometry.

For a simple example, consider two small masses connected by a rigid rod, that are freely falling in the gravitational field of a planet, and separated radially (i.e., one at a slightly higher altitude than the other). The spacetime geometry is such that, if the two masses were freely falling, their separation would increase; but the rigid rod's proper length will be constant (at least up to some point determined by the strength of the material), so at least one mass will not be freely falling and will experience a force pulling it towards the other mass; the strength of the force will be determined by the spacetime geometry, i.e., tidal gravity (how quickly the freely falling worldlines diverge). (In fact I would expect both masses to experience a force, since the rod's center of mass is what would be expected to follow a freely falling worldline.)

- #8

1977ub

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Does the spacetime curvature produced by an object affect the object itself?

One answer would be:

No, but spacetime curvature produced by part of an object can affect another part.

- #9

WannabeNewton

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1977ub said:No, but spacetime curvature produced by part of an object can affect another part.

The space-time curvature of a point-particle does back-react on the particle; here there are no internal degrees of freedom so your answer would not hold. The same thing happens in EM for a point charge so this isn't special to GR. It's just more complicated in the latter case.

- #10

loislane

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How does GR handle point-masses? My understanding is that the full non-linear theory can't do it in principle, one has to use idealized test particles without bacreaction.WannabeNewton said:The space-time curvature of a point-particle does back-react on the particle; here there are no internal degrees of freedom so your answer would not hold. The same thing happens in EM for a point charge so this isn't special to GR. It's just more complicated in the latter case.

- #11

1977ub

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WannabeNewton said:The space-time curvature of a point-particle does back-react on the particle; here there are no internal degrees of freedom so your answer would not hold. The same thing happens in EM for a point charge so this isn't special to GR. It's just more complicated in the latter case.

I interpret "an object" to be not the same as a point-particle. Perhaps the spirit of the OP is to treat them the same.

Spacetime curvature is the idea that the fabric of space and time is not flat and can be bent by the presence of massive objects, such as planets or stars.

Spacetime curvature affects objects by causing them to follow curved paths in the presence of massive objects. This can be seen in the way that planets orbit around stars, as their paths are affected by the curvature of spacetime caused by the star's mass.

Yes, spacetime curvature can be observed through the effects it has on objects. For example, the bending of light around massive objects, known as gravitational lensing, is a result of spacetime curvature.

Einstein's theory of general relativity explains the concept of spacetime curvature and how it is caused by the presence of mass and energy. It is considered one of the most accurate theories for understanding the behavior of gravity.

Yes, spacetime curvature can be measured through various methods, such as the use of gravitational lensing, the observation of the motion of planets and stars, and the detection of gravitational waves. These measurements provide evidence for the existence and effects of spacetime curvature.

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