Gravitation In Higher Dimensions

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SUMMARY

Gravitation in higher dimensions is hypothesized to follow a 1/d^(n-1) law, diverging from the behavior observed in three dimensions. In three-dimensional space, the gravitational attraction of a uniformly dense sphere is equivalent to that of a point mass at its center. However, for dimensions greater than three, this equivalence does not hold. To explore these concepts further, the gravitational shell theorem serves as a foundational model for understanding gravitational interactions in n-dimensional spaces.

PREREQUISITES
  • Understanding of gravitational laws in physics
  • Familiarity with the gravitational shell theorem
  • Basic knowledge of integration techniques
  • Concepts of dimensional analysis in physics
NEXT STEPS
  • Research the gravitational shell theorem in detail
  • Study integration techniques applicable to n-dimensional spaces
  • Explore the implications of gravitation in dimensions greater than three
  • Investigate mathematical models for gravitational forces in higher dimensions
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Physicists, mathematicians, and students interested in theoretical physics, particularly those exploring gravitational theories in higher-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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renormalize said:
Google "gravitational shell theorem".
Bingo.
 

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