The way to think about it (ignoring GR effects, I don't know how to put a metric in here...) is to consider the two mouths are identified by some map
Suppose in mouth 1 I have points labelled by postions (x1,y1,z1) and in mouth 2 I have points labelled (x2,y2,z2)
We can identify them by doing x1=x2, y1=y2, z1=z2
That means, anything that touches a point x1,y1,z2 on the spherical surface of one of the mouth, must be mapped to its corresponding position on another mouth
As we move the mouths closer to brought them to intersect
one portion of mouth 2 will touch and then penetrate into part of mouth 1
But we have said earlier that as soon anything touches one of the mouths, it must map into the corresponding position of the other
So when the left side of the blue mouth enters the right side of the red mouth, that portion has to be mapped to the right side of the blue mouth
and and the same time, the right portion of the red mouth will get mapped to the left portion of the red motuh since it enters the right potion of the blue mouth
So as the portals continue to move closer, the mapped hemispheres continues to grow.
Now at this point, one interesting question to ask is, what happens when you enter one of these hemipsheres. well we can always follow the mapping. for example
1. Suppose I enter the blue hemisphere that is produced by the two portals intersecting on the right.
2. If the portals are not intersecting, you will expect to emerge in the right end of the red mouth.
3. Howeever, because the portals intersect, the right end of the red motuh is instantly mapped to the left end of the blue mouth, which because of the intersection, instantly mapped to the left end of the red mouth.
4. Therefore the overall result is that if you enter that blue hemisphere, you must emerge at the red and vise versa
Now, at the limiting case where the two portals coincide, the two hemispheres grew completely and enveloped the region where the mouths shoudl be, so you end up with something that look like a dipole,
where if you enter the red, you will emerge at the antipodal location of the blue
Now at this point, the portals can be pushed no further, because when you follow each point with the mappings, you found they are all fixed points
in particular, the centre of the portals must map to the centre of the other, so when they collide, they can go no further as thy are both mapped to the same spot
The fixed point of this mapping thus (expected to) create a physical effect as if two rigid bodies bump into each other, like a ball hitting a wall and can go no further
Moving charged particle produces a magnetic field. If a gravitational wave passes by stationary charged particle and makes it oscillate together with the space, would that movement produce an EM wave?
