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Gravitational force in different dimensions

  1. Sep 29, 2010 #1
    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.
  2. jcsd
  3. Sep 29, 2010 #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.
  4. Sep 29, 2010 #3


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    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:
    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:
    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. "
    Last edited: Sep 29, 2010
  5. Sep 29, 2010 #4


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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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