Space Probe vs the Sun - Relativistic Frames of Reference

[Loudzoo]

Thanks Naty1 - that is encouraging ! I guess explaining concepts in simplified english will never be a substitute for the mathematics.

It now makes sense to me that all forms of energy will affect gravitational attraction in GR. What I'd be really keen to understand is how it affects the gravitational attraction in GR. In light of your suggestion, perhaps if I rephrase my previous question - DH, Dalespam or another expert might be able to elaborate ?

Are the following statements true ?
1) Increasing the kinetic energy in the form of heat of a body increases its gravitational attraction to another body
2) Increasing the kinetic energy in the form of rotational energy of a body increases its gravitational attraction to another body
3) Increasing the kinetic energy in the form of relative velocity of a body increases its gravitational attraction to another body

P.S. Happy to take advice on whether we should start a new thread on this . . .

 

[Dale]

when Dalespam says above ... I think he means..."not JUST mass".

Yes, thanks for the clarification.

 

[Dale]

Are the following statements true ?
1) Increasing the kinetic energy in the form of heat of a body increases its gravitational attraction to another body

Yes. This changes the time-time component of the stress energy tensor without changing any other component.

2) Increasing the kinetic energy in the form of rotational energy of a body increases its gravitational attraction to another body

Here it already gets more complicated. Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.

This is where the distinction between Newtonian physics and GR emerges. In Newtonian physics there would be no difference because the scalar mass density is unchanged, but in GR there is a difference because other components of the tensor have changed. In Newtonian physics this would still be a spherically symmetric problem, but in GR it is now an axisymmetric problem.

3) Increasing the kinetic energy in the form of relative velocity of a body increases its gravitational attraction to another body.

Similar as with 2).

 

[Naty1]

Dalespam:

Here it already gets more complicated. Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.

Loudzoo:
"It now makes sense to me that all forms of energy will affect gravitational attraction in GR.."

Exactly...Even PRESSURE affects gravitational attraction...

If you compress a jack in the box spring, the stored potential energy , not previously present, results in an increase in gravitational attraction accoording to the Einstein field equation. But, a very very tiny imperceptible effect.


Dalespam:

Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.

So both space and time is seen to change in the Einstein Field Equations...

Ok, so as a learning tool, can we explain to me and Loudzoo how this relates to frame dragging... frame dragging and geodetics:

from wikipedia:

"Rotational frame-dragging (the Lense–Thirring effect) appears in the general principle of relativity and similar theories in the vicinity of rotating massive objects

" Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the "rotational" effect, ...]

Static mass increase is a third effect noted by Einstein in the same paper.[5] The effect is an increase in inertia of a body when other masses are placed nearby. While not strictly a frame dragging effect (the term frame dragging is not used by Einstein), it is demonstrated by Einstein to derive from the same equation of general relativity. ...

http://en.wikipedia.org/wiki/Frame_dragging

and:

The term geodetic effect has two slightly different meanings as the moving body may be spinning or non-spinning.

SO: Non-spinning bodies move in geodesics, which is what is usually discussed in these forums, whereas spinning bodies move in slightly different orbits.

So it seems a rotating body move through spacetime just a bit differently than a non rotating body...In general this seems to make some sense since the energy is likely different.

Does a rotating body move through SPACE slightly differently??..Based on Dalespam's post above the answer seems YES since "spacial compnents" vary, right?

Is frame dragging the same as, or only a portion of, how we describe the change in
spacetime due to rotational energy? Seems like the whole thing, right?

 

[Loudzoo]

Yes. This changes the time-time component of the stress energy tensor without changing any other component.

Here it already gets more complicated. Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.

This is where the distinction between Newtonian physics and GR emerges. In Newtonian physics there would be no difference because the scalar mass density is unchanged, but in GR there is a difference because other components of the tensor have changed. In Newtonian physics this would still be a spherically symmetric problem, but in GR it is now an axisymmetric problem.

Similar as with 2).

Thanks DaleSpam and Naty1. I take from the above that different manifestations of increased kinetic energy will affect the magnitude of the increase in gravitational attraction to different degrees.
But would it be possible to summarise that in GR, an increase in the kinetic energy of a body increases its gravitational attraction to another body ?

 

[Dale]

Not in general, no. For example, if two equal-mass objects inertially moving parallel to each other at the same speed pass a stationary massless observer at t=0 then they will collide at some t=T according to the massless observer. This time T will be greater the faster the masses are moving, meaning that the gravitational attraction has decreased.

Remember, the sign of the metric is opposite for the timelike and spacelike terms, so you generally expect the timelike and spacelike components to have somewhat opposite effects. Of course, even that is a big oversimplification and I am sure there are counterexamples.

 

[Loudzoo]

Not in general, no. For example, if two equal-mass objects inertially moving parallel to each other at the same speed pass a stationary massless observer at t=0 then they will collide at some t=T according to the massless observer. This time T will be greater the faster the masses are moving, meaning that the gravitational attraction has decreased.

Remember, the sign of the metric is opposite for the timelike and spacelike terms, so you generally expect the timelike and spacelike components to have somewhat opposite effects. Of course, even that is a big oversimplification and I am sure there are counterexamples.

That example is helpful -thank you.

Presumably, if the massless observer was positioned on one of the objects she would not witness any relativistic effects given the zero relative velocity between the two objects (at least until they started gravitating towards each other) ?

To go back to the core of my original thread question: Assume two objects are moving away from each other with a significant relative velocity. Does an observer located on either object register an increase in gravitational attraction between the two bodies ?