# The relationship between Stress-Energy tensor and Mass

by Shyan
Tags: mass, relationship, stressenergy, tensor
 P: 697 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
 Sci Advisor HW Helper P: 11,834 Volumic mass density is the 00 component of the stress-energy tensor.
P: 1,618
 Quote by 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
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 $T^{\alpha \beta}$ are:
$T^{0 0} = \rho$, where $rho$ is the mass-energy density, and
$T^{1 1} = T^{2 2} = T^{3 3} = p$, where $p$ is the pressure.

P: 2,470

## The relationship between Stress-Energy tensor and Mass

 Quote by dextercioby Volumic mass density is the 00 component of the stress-energy tensor.
Energy density, which is proportional to mass density only for a body at rest.
 P: 697 Thanks guys But what about other components?
P: 1,618
 Quote by Shyan Thanks guys But what about other components?
As I said, for a fluid at rest, the three spatial components of the stress-energy tensor are just the pressure.
Mentor
P: 11,052
 Quote by Shyan But what about other components?
The diagram on the Wikipedia page identifies what the various components (or groups of them) represent.
P: 284
 Quote by Shyan Thanks guys But what about other components?
In addition to what Steven said, the off diagonal terms are shear stresses.
 Emeritus Sci Advisor P: 7,371 And of course you have momentum density....if you have a moving object or fluid.

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