Comment on 'Reexamining $f\left(R,T\right)$ gravity', Phys. Rev. D 100, 064059 (2019)

In a recent paper, "Reexamining $f\left(R,T\right)$ gravity", by S. B. Fisher and E. D. Carlson, Phys. Rev. D 100, 064059 (2019), the authors claim that for the particular $f(R,T)$ modified gravity model, with $f(R,T)=f_1(R)+f_2(T)$, the term $f_2(T)$ must be included in the matter Lagrangian and therefore it does not have any physical significance. We carefully reexamine the line of reasoning presented in the paper, and we show that there are several major conceptual problems related to the author's physical interpretations, as well as in the physical and mathematical approaches used to derive the energy-momentum tensor of the theory. These problems raise some serious concerns about the validity of most of the results presented in the paper.
Comment: 4 pages, no figures, accepted for publication in PRD