Opposite Side of GR: Is it Possible?

[zonde]

"Opposite side" of GR

I am trying to consider kind of "opposite side" of GR.
Let's consider some area in space where density of matter is less then average density of matter across the universe and in every direction average density of matter can be viewed as being higher than at this particular place.
Then gravity in this area would be repulsive, right? Light will bend away from that area and matter will "fall out" of this place.

Is it possible to find some description of that place similar to GR description for gravitating body. Let's say we make necessary assumptions about symmetry of this situation.
Something like smoothing out of topology as you approach center contrary to bending?

 

[Ich]

Then gravity in this area would be repulsive, right?

No, it would be weaker or absent.
I think you intend to express the underdensity as repulsive gravity superimposed on the attractive gravity background. You can do that in the Newtonian approximation (where superposition works), but the effect would never be light bending outwards. It will bend less inwards, that's all.

 

[PAllen]

I think in Newtonian approximation, the OP idea can be correct, in some sense. Not that gravity is repulsive inside the low density bubble, but that the bubble acts, to some extent, as a repulsor. A mass passing near the bubble will experience stronger gravity on its side away from the bubble, so will bend away from the bubble.

 

[zonde]

I think in Newtonian approximation, the OP idea can be correct, in some sense. Not that gravity is repulsive inside the low density bubble, but that the bubble acts, to some extent, as a repulsor. A mass passing near the bubble will experience stronger gravity on its side away from the bubble, so will bend away from the bubble.

It seems that in Newtonian approximation it should not work.
Look we can compare superposition of gravity sources with electric charge. Electric charge inside sphere where charge is evenly distributed on the surface of sphere is zero. Now as we add bigger and bigger charged surfaces of spheres (up to infinity) they would still not change field inside hollow sphere - still zero.

So with Newtonian approximation we would require some entity that possesses opposite charge of gravity i.e. antigravitating entity.

 

[PAllen]

It seems that in Newtonian approximation it should not work.
Look we can compare superposition of gravity sources with electric charge. Electric charge inside sphere where charge is evenly distributed on the surface of sphere is zero. Now as we add bigger and bigger charged surfaces of spheres (up to infinity) they would still not change field inside hollow sphere - still zero.

So with Newtonian approximation we would require some entity that possesses opposite charge of gravity i.e. antigravitating entity.

You misundestood my description. A charged sphere is not the right EM analog. The right analog would be a diffuse fluid with positive charge distributed throughout, and a bubble of no charge. What happens as a negative test particle (that, for some reason, cannot be neutralized by picking up positive charges) passes near the bubble?

The key point, in my original post, is what happens to a particle passing near the low density bubble, *outside* the bubble, not inside the bubble.

However, the Newtonian analog, as described, is simpler because of the absence of positive and negative masses. It should work as described. Read the scenario more carefully.

 

[zonde]

You misundestood my description. A charged sphere is not the right EM analog. The right analog would be a diffuse fluid with positive charge distributed throughout, and a bubble of no charge. What happens as a negative test particle (that, for some reason, cannot be neutralized by picking up positive charges) passes near the bubble?

The key point, in my original post, is what happens to a particle passing near the low density bubble, *outside* the bubble, not inside the bubble.

However, the Newtonian analog, as described, is simpler because of the absence of positive and negative masses. It should work as described. Read the scenario more carefully.

Yes you are right, charged sphere is not the right analog.
If I have not made some error then it seems that even inside the bubble is different then in charged sphere analog.