# Stress energy tensor from equations of motion

In field theory, if you are given an action $S$, the standard way to find the stress energy tensor is $$T^{\mu\nu}= -\frac{2}{\sqrt g}\frac{\delta S}{\delta g^{\mu\nu}}.$$ But there are many examples of classical equations of motion that cannot be derived from an action (take first order hydrodynamics as an example). My question is: If you only know the equations of motion of a system (and no corresponding action exists), how do you find the stress energy tensor?

• – Qmechanic Jul 7 '18 at 5:48
• See the rayleigh-plessot equation. – user97261 Jul 7 '18 at 11:44