Curvature of Space-time

[Freeman]

I have a quick question about the curvature of space-time equation, well two questions.

 

1. What is "k" on the right hand side of the equation (the equation I am referring to is the curvature tensor equals eight pi multiplied by "k" multiplied by the stress energy tensor).

 

2. What is the stress energy tensor?

 

I know the second question is really an uber-simpleton one, but it's been on my mind for a while now...

[□h=-16πT]

k is [math]\frac{G}{c^4}[/math], I think that's what you're refering to. The tensor you call the curvature tensor isn't actually THE curvature tensor, it's a tensor constructed from contractions of the Riemann curvature tensor that automatically conserves energy-momentum, but it does essentially give the curvature.

 

For a fluid the SE tensor describes the dyamics of the system, i.e. energy-density, energy-flux, momentum-density, momentum-flux etc.

 

One definition that you may find for a general SE tensor is

 

[math]

T^{\mu\nu}=\frac{1}{\sqrt{-g}}\frac{dS}{dg^{\mu\nu} }

[/math]

 

Where [math]g^{\alpha\beta}[/math] is the metric, g is its determinant and S is the action for the system.

[□h=-16πT]

Does that answer your question, or would you like a better explanation?

[Freeman]

That answers my question. Thanks for the help!

[□h=-16πT]

You're welcome .