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Forums
Physics
Special and General Relativity
Going from Cauchy Stress Tensor to GR's Energy Momentum Tensor
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[QUOTE="vanhees71, post: 6848856, member: 260864"] In relativistic physics, the "Cauchy stress tensor" form the space-space components of the energy-momentum tensor. The time-time component is the energy density and the time-space components are the momentum density (times ##c##). The interesting thing with GR is that when you take the "mechanical energy momentum tensor" (ideal/viscous fluids, elastic bodies,...) on the right-hand side if you have a solution of the Einstein equations, due to the Bianchi identities the equations of motion for the matter, which is given by ##\vec{\nabla}_{\mu} T^{\mu \nu}=0## is automatically fulfilled, i.e., you can get a fully consistent solution of the Einstein equations only if you simultaneously solve the mechanics equations of motion for the matter. A very nice treatment of all this can be found in D. E. Soper, Classical Field Theory [/QUOTE]
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Physics
Special and General Relativity
Going from Cauchy Stress Tensor to GR's Energy Momentum Tensor
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