Gravitational force in different dimensions

  • Thread starter pavi_elex
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  • #1
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Main Question or Discussion Point

How Gravitational force differs in different dimensions.
what it would be for four dimensions, two dimensions and one dimension.
Give me the formula of Gravitational force in n dimension space.
If it is described well (complete derivation) in other web site, send me the link.
 

Answers and Replies

  • #2
George Jones
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Look at chapter 3 (including exercises and problems) from A First Course in String Theory by Barton Zwiebach.
 
  • #3
atyy
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(2+1)D:
http://arxiv.org/abs/gr-qc/9503024
Lectures in (2+1)-Dimensional Gravity
Steven Carlip
"Work on (2+1)-dimensional gravity dates back at least to 1963 [1], and occasional articles appeared over the next twenty years [2, 3, 4]. But credit for the recent growth of interest should probably go to two groups: Deser, Jackiw, and ’t Hooft [5,6,7], who examined the classical and quantum dynamics of point sources, and Witten [8, 9, 10], who rediscovered and explored the representation of (2+1)-dimensional gravity as a Chern-Simons theory.*
*The Chern-Simons representation was first pointed out, I believe, by Achucarro and Townsend."

(2+1)D versus (3+1)D:
http://arxiv.org/abs/gr-qc/9905087
An Introduction to Spin Foam Models of Quantum Gravity and BF Theory
John C. Baez
"In particular, general relativity in 3 dimensions is a special case of BF theory, while general relativity in 4 dimensions can be viewed as a BF theory with extra constraints. ........... unlike BF theory, general relativity in 4 dimensions has local degrees of freedom."

(3+1)D versus (4+1)D:
http://arxiv.org/abs/hep-th/0608012
Black Rings
Roberto Emparan, Harvey S. Reall
"A black ring is a five-dimensional black hole with an event horizon of topology S1 x S2. We provide an introduction to the description of black rings in general relativity and string theory. Novel aspects of the presentation include a new approach to constructing black ring coordinates and a critical review of black ring microscopics. "
 
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  • #4
tom.stoer
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For space dimension D=3, 4, ... it's U(r) ~ 1/rD-2;

Basically this can be understood via solving a Poisson equation for the D-dim. laplacian. Doing this in momentum space one finds a Greens function ~ 1/k². The potential U(r) is the Fourier transform of this Greens function which is ~ 1/rD-2, therefore the force is div U(r) ~ 1/rD-1.

This calculation is exact in D-dim. Maxwell theory, but only approx. valid in ART as one has to use the Newtonian limit in order to arrive at the Poisson equation.
 

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