Are conservation laws independent of field equations?

Abstract

The charge conservation law (${\partial }_{\alpha }{J}^{\alpha }=0$) usually is considered as a corollary of Maxwell's equations and is not independent of Maxwell's field equations. A circular reasoning, however, is found in the derivation. A similar fallacy exists in the matter source's conservation law (${\nabla }^{\mu }{T}_{\mu \nu }=0$) and Einstein's field equations. Therefore, the source's conservation laws are independent of Einstein's field equations.

arXiv comment3 pages