divergenceless

Thus can be written as a combination of a scalar and a divergenceless, two-component vector.

The Noether current is defined up to a solenoidal (divergenceless) vector field.

When the velocity vector in this phase space is divergenceless, then the equations of motion reduce to those obtained by Nambu.

This current is a bound current, not having any charge accumulation associated with it since it is divergenceless.

The generalized phase-space velocity is divergenceless, enabling Liouville's theorem.

The result is the divergenceless second-rank Einstein tensor where R is the Ricci scalar.

An immediate consequence of this ansatz is that should be a symmetric divergenceless second-rank tensor to match the stress-energy tensor.

The proof that the Einstein tensor is both symmetric and divergenceless is given in Appendix B. Like its progenitors, the Riemann and Ricci tensors, the Einstein tensor vanishes in the absence of any material to warp space-time.