= Scalar stress-energy divergence identity
{title2=$\nabla^aT_{ab}=(\Box\phi-V^{\prime}(\phi))\nabla_b\phi$}
For a <minimally coupled scalar field> with a <Levi-Civita connection>, <metric compatibility> and the <symmetric Hessian of a scalar field> give the displayed off-shell identity. It is a special case of the <diffeomorphism Noether identity for a scalar field>, and gives <stress-energy conservation> when the scalar equation is satisfied. No gravitational field equation is needed.
Back to article page
