The relationship between Stress-Energy tensor and Mass


by Shyan
Tags: mass, relationship, stressenergy, tensor
Shyan
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#1
Dec9-12, 07:28 AM
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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
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dextercioby
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Dec9-12, 07:49 AM
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Volumic mass density is the 00 component of the stress-energy tensor.
stevendaryl
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Dec9-12, 07:50 AM
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Quote Quote by Shyan View Post
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 [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
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Dec9-12, 10:15 AM
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The relationship between Stress-Energy tensor and Mass


Quote Quote by dextercioby View Post
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.
Shyan
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Dec9-12, 11:16 PM
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Thanks guys
But what about other components?
stevendaryl
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Dec12-12, 11:06 AM
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Quote Quote by Shyan View Post
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.
jtbell
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Dec12-12, 12:33 PM
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Quote Quote by Shyan View Post
But what about other components?
The diagram on the Wikipedia page identifies what the various components (or groups of them) represent.
cosmik debris
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Dec12-12, 02:54 PM
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Quote Quote by Shyan View Post
Thanks guys
But what about other components?
In addition to what Steven said, the off diagonal terms are shear stresses.
pervect
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Dec12-12, 03:01 PM
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And of course you have momentum density....if you have a moving object or fluid.


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