- it's not just a preprint, it was published in IOP's "Journal of Physics: Conference Series". But there are lots of questions I'd raise if I were refereeing this.
For example, how are you going to get the metric to describe gravity (as it usually does) *and* electromagnetism. I'd argue it doesn't have enough degrees of freedom to handle both. E.g. they're saying a wave of light really *is* a distortion of the geometry of spacetime, and somehow we've never noticed that.
I'd also ask what happened to the usual gauge-invariance of electromagnetism, which lets us change the A field in certain ways without changing anything physical. Their approach gives a strange equation (39), which they "simplify" (without justification) to get Maxwell's equations in Lorentz gauge (40). So are they claiming Lorentz gauge is preferred and the whole business of gauge invariance was a mistake? Strangely, I don't see any discussion of that.