Why is gravity a fictitious force?

[Demystifier]

Then you are doing quantum field theory, not classical GR. This is the classical GR forum, so here, we use the GR definition of force.

There is a classical version of this. Formulate gravity as a spin-2 field on a Minkowski background. Develop a perturbative method of classical scattering computation, which leads to classical Feynman diagrams (differing from the quantum Feynman diagrams by having no loop diagrams). The internal lines of Feynman diagrams contain Green functions (which is just a classical name for the mathematical object called propagator in quantum physics). Then you can say that the force is represented by this Green function in the classical Feynman diagram.

 

[PeterDonis]

There is a classical version of this.

This can only represent "gravitational fields" on the chosen background. It can't, for example, represent a black hole spacetime, because the global topology of that spacetime is incompatible with the Minkowski background.

Also, classically it's a weird way of doing things, because the background spacetime is unobservable--the "field" appears as a change in the spacetime geometry itself. With other QFTs, such as the Standard Model, that's not the case.