I'm sure there's a trivial explanation for this, but it's escaping me. The space-space components of the stress-energy tensor are interpreted as the 3x3 stress tensor. But WP claims that the symmetry of the stress tensor need only hold in the case of equilibrium: "However, in the presence of couple-stresses, i.e. moments per unit volume, the stress tensor is non-symmetric. This also is the case when the Knudsen number is close to one, [...] or the continuum is a non-Newtonian fluid, which can lead to rotationally non-invariant fluids, such as polymers." -- http://en.wikipedia.org/wiki/Stress...m_equations_and_symmetry_of_the_stress_tensor How can this be reconciled with the Einstein field equation's prediction that T must be symmetric (since the Einstein tensor is symmetric by definition)? Obviously polymers don't violate GR! Fundamentally, a polymer is made out of nonrelativistic matter, i.e., dust in relativistic parlance, interacting through electromagnetic fields. Dust and EM fields both have symmetric stress-energy tensors.