The relationship between Stress-Energy tensor and Mass

Shyan

In Einstein field equations,the term that is responsible for curving Space-Time is the Stress-Energy tensor.But we know that mass should be able to curve space-time.So I think every mass distribution should have a Stress-Energy tensor associated with it.
What is that relationship?
Thanks

dextercioby

Volumic mass density is the 00 component of the stress-energy tensor.

stevendaryl

The relationship is explained in Wikipedia here: http://en.wikipedia.org/wiki/Stress%...3energy_tensor

The simplest case is a perfect fluid at rest. In that case, the nonzero components of the stress-energy tensor [itex]T^{\alpha \beta}[/itex] are:
[itex]T^{0 0} = \rho[/itex], where [itex]rho[/itex] is the mass-energy density, and
[itex]T^{1 1} = T^{2 2} = T^{3 3} = p[/itex], where [itex]p[/itex] is the pressure.

K^2

Energy density, which is proportional to mass density only for a body at rest.

Shyan

Thanks guys
But what about other components?

stevendaryl

As I said, for a fluid at rest, the three spatial components of the stress-energy tensor are just the pressure.

jtbell

The diagram on the Wikipedia page identifies what the various components (or groups of them) represent.

cosmik debris

In addition to what Steven said, the off diagonal terms are shear stresses.

pervect

And of course you have momentum density....if you have a moving object or fluid.