Reexamining $f(R,T)$ Gravity

In $f(R,T)$ gravity, the gravitational contribution to the action is generalized from $R$ to an arbitrary function of the curvature $R$ and the trace of the stress-energy tensor $T$. Such theories have been studied and limits place on the parameters using a variety of physical systems. But these studies rely on a non-physical separation of the matter Lagrangian ${\cal L}_m$ from the gravitational contribution. We illustrate the artificial nature of this separation with a specific example and suggest a convention for avoiding such confusion in the future.