I Gravitation In Higher Dimensions

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Gravitation in higher dimensions is believed to follow a 1/d^(n-1) law, differing from the 3D case where a uniformly dense sphere's gravitational attraction is equivalent to a point mass at its center. For dimensions greater than three, this equivalence does not hold, prompting a search for the results in those scenarios. The discussion seeks to use the known 3D integration case as a model to understand higher-dimensional gravitation. A suggestion to search for the "gravitational shell theorem" was provided as a helpful resource. Understanding these concepts is crucial for exploring gravitational dynamics in n-dimensional spaces.
Hornbein
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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?
 
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Hornbein said:
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".
 
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Likes Vanadium 50, jim mcnamara, Hornbein and 1 other person
renormalize said:
Google "gravitational shell theorem".
Bingo.
 

Thread 'Gravitational effects of a small black hole passing your body'

Abstract The gravitational effects of a Primordial Black Hole (PBH) passing through the human body are examined, with the goal of determining the minimum mass necessary to produce significant injury or death. Two effects are examined: The damage caused by a shock wave propagating outward from the black hole trajectory, and the dissociation of brain cells from tidal forces produced by the black hole on its passage through the human body. It is found that the former is the dominant effect...
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