Gravity (more precisely, a dynamical metric) is absolutely a field in the QFT sense. The problem is that its unrenormalizable. That’s a technical term that roug

Gravity (more precisely, a dynamical metric) is absolutely a field in the QFT sense. The problem is that its unrenormalizable. That’s a technical term that roughly means the theory doesn’t make predictions to arbitrarily high energies. As a result the QFT describing gravity cannot be used to answer the interesting questions about black holes and Planck-scale physics. Historically this has meant that a new physical mechanism has been ignored that becomes relevant only at large energies, such as stringy physics in string theories or discrete spacetime in LQG. That’s part of why critics argue about the falsifiability of string theory (unfortunately the same critics don’t make the obvious conclusion that unfalsifiability in this sense implies to all models of quantum gravity, not just strings—-and that’s a funding motivated lie by omission. This has to be true since by their own framework, if LQG predicts something and string theory predicts nothing, the experiment distinguishing them could falsify string theory by validating that prediction). Indeed, if gravity were not described by a QFT at low energies, we would need an extremely convoluted explanation for why quantum effects aren’t always destroyed by the mere existence of gravity. In short, gravitons are the Occam’s razor solution, not having gravitons would be extremely hard to reconcile with the existence of gravity at any scale, and when you dive into the math you see why. In any case, none of that directly answers your question about gravitoelectromagnetism, which actually is just a way to rewrite the Einstein equations in a particular way that’s valid only sometimes. And that could only be unphysical if Einstein’s equations are unphysical in the same regime. There’s no regime we’ve tested in where the Einstein equations aren’t empirically valid, and they do come naturally as the classical limit of the gravitational QFT (the limit implies there can be small corrections of a particular form, however).