Why viscosity ignores rotation: a geometric proof

Every major framework for relativistic viscous fluids shares the same assumption: viscous stress responds to shear and expansion, but not to rotation or acceleration. Working from a Lagrangian construction on curved spacetimes, the authors show this isn't an assumption at all — acceleration drops out under spatial projection and vorticity cancels by symmetry, making the structure inevitable. As a bonus, the same framework reproduces Weinberg's classic formula for gravitational-wave damping in an expanding universe directly from the geometry of fluid strain.