Applying variational principles to that metric describes a black hole!

  • Thread starter physx_420
  • Start date
  • #1
33
0

Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
33
0
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
 
  • #3
bcrowell
Staff Emeritus
Science Advisor
Insights Author
Gold Member
6,723
423
This equation was posted on a different website and the O.P said:"Applying variational principles to that metric describes a black hole!"
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.
 
  • #4
5,428
291
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]
 
  • #5
3,962
20
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.
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.
 
  • #6
bcrowell
Staff Emeritus
Science Advisor
Insights Author
Gold Member
6,723
423
Good point, kev.

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

Related Threads on Applying variational principles to that metric describes a black hole!

Replies
9
Views
863
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
308
Replies
37
Views
2K
Replies
3
Views
2K
Top