Applying variational principles to that metric describes a black hole

[physx_420]

ds^{2} = -c^{2}(1 - \frac{2Gm}{c^{2}r})dt^{2} + (1 - \frac{2Gm}{c^{2}r})^{-1} dr^{2} + r^{2}d\Omega^{2}

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^{2} = -dt^{2} + (dx - v_{s}f(r_{s}dt)^{2} + dy^{2} + dz^{2}

Does this have any implications, be they big or small? Anyone have any inputs on this?

 

[physx_420]

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

 

[bcrowell]

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.

 

[Mentz114]

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]

 

[yuiop]

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.

 

[bcrowell]

Good point, kev.

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