Gravitation In Higher Dimensions

[Hornbein]

It is assumed that gravitation in n dimensions would follow an approximate 1/d^(n-1) law. In our 3D world the attraction of a uniformly dense sphere is the same as if all the mass were concentrated at its center. I have read for n>3 this is not so. I want to find out what the result would be. I think I can do it if I have the common n=3 integration case as a model. I tried an Internet search but could not guess the correct search term. Any help?

 

[renormalize]

It is assumed that gravitation in n dimensions would follow an approximate 1/d^(n-1) law. In our 3D world the attraction of a uniformly dense sphere is the same as if all the mass were concentrated at its center. I have read for n>3 this is not so. I want to find out what the result would be. I think I can do it if I have the common n=3 integration case as a model. I tried an Internet search but could not guess the correct search term. Any help?

Google "gravitational shell theorem".

 

[Hornbein]

Google "gravitational shell theorem".

Bingo.