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Applying variational principles to that metric describes a black hole!

  1. Mar 23, 2010 #1
    ds[tex]^{2}[/tex] = -c[tex]^{2}[/tex](1 - [tex]\frac{2Gm}{c^{2}r}[/tex])dt[tex]^{2}[/tex] + (1 - [tex]\frac{2Gm}{c^{2}r}[/tex])[tex]^{-1}[/tex] dr[tex]^{2}[/tex] + r[tex]^{2}[/tex]d[tex]\Omega[/tex][tex]^{2}[/tex]

    This equation was posted on a different website and the O.P said:"Applying variational principles to that metric describes a black hole!"

    I was wondering if anyone could explain it a little better. Also, to anyone knows who Miguel Alcubierre is (the guy that created an equation for a hypothetical warp-drive); the above equation shows some similarities to his:

    ds[tex]^{2}[/tex] = -dt[tex]^{2}[/tex] + (dx - v[tex]_{s}[/tex]f(r[tex]_{s}[/tex]dt)[tex]^{2}[/tex] + dy[tex]^{2}[/tex] + dz[tex]^{2}[/tex]

    Does this have any implications, be they big or small? Anyone have any inputs on this?
     
  2. jcsd
  3. Mar 23, 2010 #2
    in M. Alcubierre's equation the "s" in the superscript of "v and r" are supposed to be subscripts, I just couldn't get them to work. btw
     
  4. Mar 23, 2010 #3

    bcrowell

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    Unless I'm missing something, you can cut the part about "Applying variational principles to..." The correct statement would simply be: "[T]hat metric describes a black hole!" This is simply the standard form of the Schwarzschild metric, as far as I can see.
     
  5. Mar 23, 2010 #4

    Mentz114

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    The first metric you show is the Scwarzschild exterior of a radially symmetric source with a singularty at r=0 and a horizon at r=2GM/c^2.

    Look up 'Scwarzschild metric' on Wiki.

    [Ben - snap]
     
  6. Mar 23, 2010 #5
    I think we should acknowledge that the standard Schwarzschild metric can also represent the vacuum region outside a regular non-rotating uncharged non-singular massive body that is not a black hole.
     
  7. Mar 23, 2010 #6

    bcrowell

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    Good point, kev.

    Lut, what does "[Ben - snap]" mean???
     
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