The field theoretic approach to GR is generally considered overlooked by philosophers (who have, on this narrative, rather focused on the geometrical representation of gravity). The claim is, however, only half-true as much depends on what one takes the field theoretic approach to begin with.
Especially with respect to quantum gravity, many approaches, including the major contenders string theory and loop quantum gravity (but also for instance in the asymptotic safety program) stress the parallels if not potential for unification of gravity with the other interactions.
Often, the field theoretic approach is associated with a particle physics tradition — in the spirit of Feynman, Weinberg, and Dese (among others). But even that seems a bit too simple: loop quantum gravity has many parallels to QCD, say; and GR has traditionally been considered in analogy with electrodynamics from very early on.
In the philosophy of physics literature, the field theoretic approach to GR (and, more specifically, a Minkowski-background-based spin-2 approach) as treated in philosophy are line with particle physicis. (Pitts, however, has worked out over the years how much of a gray-area there is between a clear field theoretic (in the particle physics sense), and a clear geometrical perspective.)
Petrov and Pitts characterize field theory approaches at a general level as splitting up the metric into static background, and dynamical perturbation (not necessarily small!) — with appropriately adapted Lagrangian dynamics. Thus formulated, the field theoretic approach is effectively equivalent to GR; at the price of an unphysical (gauge) background metric, various usually desirable features are achieved: (coordinate-dependent) gravitational energy-momentum tensors; possibility to formulate the Schwarzschild mass via a delta-distribution (in specific gauge).\footnote{Cf. to even in electrodynamics, only a specific gauge makes the Coulom terms explicit.} It seems Petrov and Pitts see various representational advantages of the field theoretic approach. Then, again, in some other work, Pitts pushes a Minkowski-background specific approach where the background is only to be understood as vacuum. Here, Pitts seems to make for what structure precisely represents spacetime. Similarly, Salimkhani uses the claims in the literature of a Minkowski-background based derivation of GR for arguing for an ontological reduction. In contrast, Linnemann, Smeenk, and Baker propose understanding the derivation in an epistemic (heuristic) fashion.Yet another suggestion is that of providing a partial interpretation \citep{Schneider}.
Especially with respect to quantum gravity, many approaches, including the major contenders string theory and loop quantum gravity (but also for instance in the asymptotic safety program) stress the parallels if not potential for unification of gravity with the other interactions.
Often, the field theoretic approach is associated with a particle physics tradition — in the spirit of Feynman, Weinberg, and Dese (among others). But even that seems a bit too simple: loop quantum gravity has many parallels to QCD, say; and GR has traditionally been considered in analogy with electrodynamics from very early on.
In the philosophy of physics literature, the field theoretic approach to GR (and, more specifically, a Minkowski-background-based spin-2 approach) as treated in philosophy are line with particle physicis. (Pitts, however, has worked out over the years how much of a gray-area there is between a clear field theoretic (in the particle physics sense), and a clear geometrical perspective.)
Petrov and Pitts characterize field theory approaches at a general level as splitting up the metric into static background, and dynamical perturbation (not necessarily small!) — with appropriately adapted Lagrangian dynamics. Thus formulated, the field theoretic approach is effectively equivalent to GR; at the price of an unphysical (gauge) background metric, various usually desirable features are achieved: (coordinate-dependent) gravitational energy-momentum tensors; possibility to formulate the Schwarzschild mass via a delta-distribution (in specific gauge).\footnote{Cf. to even in electrodynamics, only a specific gauge makes the Coulom terms explicit.} It seems Petrov and Pitts see various representational advantages of the field theoretic approach. Then, again, in some other work, Pitts pushes a Minkowski-background specific approach where the background is only to be understood as vacuum. Here, Pitts seems to make for what structure precisely represents spacetime. Similarly, Salimkhani uses the claims in the literature of a Minkowski-background based derivation of GR for arguing for an ontological reduction. In contrast, Linnemann, Smeenk, and Baker propose understanding the derivation in an epistemic (heuristic) fashion.Yet another suggestion is that of providing a partial interpretation \citep{Schneider}.