Yeah, I think so too. While the authors might attempt to counter that they are only describing EM in vacuum, the fact is that GR is nonlinear. You can’t just add an EM sector by a rank-1 metric component and expect linearity to apply.
At some level, this feels like a vacuous result. If you start with a rank-2 massless field theory, and constrain it to act on rank-1 fields, is it surprising that you get a rank-1 massless field theory? Is this not just an elaborate form of completing the square?
At some level, this feels like a vacuous result. If you start with a rank-2 massless field theory, and constrain it to act on rank-1 fields, is it surprising that you get a rank-1 massless field theory? Is this not just an elaborate form of completing the square?