Gravitation In Higher Dimensions

  • #1
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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  • #2
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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  • #3
renormalize said:
Google "gravitational shell theorem".
Bingo.
 

FAQ: Gravitation In Higher Dimensions

What is meant by "higher dimensions" in the context of gravitation?

In the context of gravitation, "higher dimensions" refer to spatial dimensions beyond the familiar three (length, width, and height). Theories such as string theory and certain models of cosmology propose that additional spatial dimensions exist, which could be compactified or extended, influencing gravitational behavior and the fundamental structure of the universe.

Why study gravitation in higher dimensions?

Studying gravitation in higher dimensions can provide insights into fundamental physics, including the unification of forces, the nature of black holes, and the early universe's conditions. It also offers potential solutions to unresolved issues in standard theories, such as the hierarchy problem in particle physics and the nature of dark matter and dark energy.

How does gravity behave differently in higher dimensions?

In higher dimensions, the behavior of gravity changes significantly. For example, the gravitational force may follow different inverse power laws, depending on the number of dimensions. This can lead to different predictions for the behavior of gravitational fields, the structure of black holes, and the dynamics of cosmological models.

What are some theoretical models that incorporate higher-dimensional gravitation?

Several theoretical models incorporate higher-dimensional gravitation, including string theory, M-theory, and braneworld scenarios. These models propose mechanisms by which additional dimensions can be compactified or hidden from direct observation, while still influencing physical phenomena at fundamental levels.

Are there any experimental or observational evidences for higher dimensions?

Currently, there is no direct experimental or observational evidence for higher dimensions. However, researchers are investigating potential indirect signs, such as deviations from Newtonian gravity at small scales, effects on cosmic microwave background radiation, and signatures in particle collisions at high energies. Future experiments and observations may provide more clues about the existence of higher dimensions.

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