# Does the curvature produced by an object affect itself?

1. Jul 16, 2015

### ORF

Hello

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

Greetings!

2. Jul 16, 2015

### PAllen

Yes. Consider the extreme case assembling more and more matter together. Even keeping the overall density to be e.g. that of water, as long as you can, at some point you get catastrophic collapse, forming a black hole. This is clearly a case of spacetime curvature acting on the matter that is causing the curvature.

3. Jul 16, 2015

### WannabeNewton

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

4. Jul 19, 2015

### Mueiz

No..The spacetime curvature pruduced by an object cannot affect the object itself ..What is mentioned in the answer above correct but this related to the effects of
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. Jul 19, 2015

### PAllen

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.

Last edited: Jul 19, 2015
6. Jul 19, 2015

### 1977ub

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. Jul 19, 2015

### Staff: Mentor

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. Jul 19, 2015

### 1977ub

What I'm suggesting is that for the question:
Does the spacetime curvature produced by an object affect the object itself?

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

9. Jul 19, 2015

### WannabeNewton

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. Jul 19, 2015

### loislane

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.

11. Jul 19, 2015

### 1977ub

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.