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The Stress part of the Stress  Energy  Momentum Tensor 
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#1
Dec1910, 09:08 AM

C. Spirit
Sci Advisor
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Hey guys I'm having trouble understanding the full nature of the energy momentum tensor. I understand the whole "matter flow and energy flow" affects the curvature of the space time metric being used. What I don't understand is the role of stress and shear  stress. Is the stress being described the stress that the mass places on space  time? Thanks.



#2
Dec1910, 03:16 PM

P: 239

Also remember, that pressure is the external push and stress is internal and pull. So we can think of pressure as T11, T22, and T33. Ever component against itself that does not include energy density is stress. Energy density, pressure, and stress also have the same units. Energy density = Energy / Area * Distance Energy density = Force * Distance / Area * Distance Energy density = Force / Area Pressure = Force / Area Stress = Force / Area 


#3
Dec1910, 06:57 PM

C. Spirit
Sci Advisor
Thanks
P: 5,637

Cool thanks. Just another quick (kind of unrelated) question:
If one wants to solve the field equations for a particular Energy Momentum Tensor then would one introduce that tensor into the equations solving for the metric? I'm asking because doesn't the metric also determine energy  momentum distribution? Or do you use a metric that would best suit the kind of mass distribution you wish to solve for and then solve to find the metric of the space  time with that specific mass distribution? (Like in the case of the schwarzschild metric where you use static spherical mass distribution and the metric for spherical coordinates)  sorry for sounding like a completely confused idiot. 


#4
Dec1910, 10:31 PM

P: 3,967

The Stress part of the Stress  Energy  Momentum Tensor



#5
Dec2010, 06:49 AM

P: 1,115




#6
Dec2010, 10:06 PM

P: 3,967

It states that "[itex] T^{ii}[/itex] (not summed) represents normal stress which is called pressure when it is independent of direction." where i ranges from 1 to 3 as indicated by the diagonal green "pressure" band in the diagram. These may be a key observation. The "biaxial" forces in the shell are classed as stress, but if the forces are equal in all directions then it is classed as pressure. Would I be right in thinking that if [itex] T^{11}=T^{22}= T^{33}[/itex] then that represents pressure, but if those elements are not equal, then it represents stress? Wikipedia also states the orange triangular sections of the tensor diagram [itex]T^{ik}, \quad i \ne k[/tex] represents shear stress so the shear stress components are distinct from the normal stress components. The same components are sometimes described as viscosity in other references and presumably the distinction depends on whether we are talking about solids or liquids, even though that distinction is not always clear cut. Wikipedia also hints that the "box" labelled "momentum flux" in the above diagram is basically the same as the stress tensor used in engineering. Also, if we had a large planet sized sphere, would I be right that in thinking that a stressenergy tensor cannot represent the whole object but just some small finite (infinitesimal?) element of the large object? Is a metric basically the result of summing numerous stressenergy tensors that make up the composite whole? 


#7
Dec2110, 08:10 AM

P: 1,115




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