Geoffrey MillerVerified account

(Early) Friday physics fun: it turns out that the inverse square law for electromagnetism and gravity is not true for spheres getting close to each other. http://aleph.se/andart2/physics/when-the-inverse-square-stops-working/ …

The gravitational case happens because the spheres deform into ellipsoids and hence have parts closer to each other than they "should" be.

One might complain that for perfectly rigid spheres this is not an issue but real material spheres are not rigid. Planets and moons largely behave like liquid droplets. In special and general relativity perfectly rigid objects are not even allowed (would have speed of sound >c).

In fact, even defining something like rigid bodies in relativity is fraught. Every point in a rigid body is supposed to remain at the same distance from every other point, but when the body moves (especially when it rotates) this fails. https://en.wikipedia.org/wiki/Born_rigidity …

For really strong gravitational fields the distance to the body gets affected by spacetime curvature, further confusing things. In black hole potentials behave as if one measured the distance in the inverse square law to the event horizon surface, not the geometric centre.

I've always wondered if six black holes could come together and form a cube. Could you isolate a region of space from the universe that way? Any strange properties?