The Importance of Symmetry in Stress Tensors

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A symmetric stress tensor is essential because a nonsymmetric tensor indicates an interior source of stress energy, as per Cauchy's second law of motion. The components of the stress-energy tensor represent energy density and momentum flows, with off-diagonal elements indicating shear stresses. In general relativity, the stress-energy tensor typically describes perfect fluids, such as dust or radiation, which have specific properties regarding pressure and shear stress. Understanding the implications of a nonsymmetric tensor is crucial for accurately modeling physical systems. This discussion highlights the importance of symmetry in stress tensors within the context of physics and general relativity.
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Why stress tensor must be symmetric?
 
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A nonsymmetric stress tensor means that there is an interior source of stress energy (Cauchy's second law of motion).
 
Some reference for this perhaps? What that means physically? -Example!
 
The T00 component of the stress energy tensor is energy density, the T11, T22, T33 (the diagonal components) are momentum flows or pressures. The off diagonals represent shear stresses and as Andy has pointed out a non-symmetric tensor means there is an interior source of energy. In GR this tensor usually represents a perfect fluid which is either dust (zero pressures) or radiation which is a fluid with pressure but no shear stress.
 
I don't understand this. Is there some other way. If \hat{N} is symmetric then \hat{N}=\hat{N}^*. Maybe from this?
 

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