On the (in)equivalence of the theories of general relativity and spin-2 gravity

Abstract

A classical result in gravitational physics concerns a relation between the theory of general relativity and the theory of a self-coupling massless spin-2 particle. It was regarded as textbook knowledge that, when the self-coupling of a particle with these properties is considered, the structure of such a nonlinear theory is that of general relativity. However, recent works have shown how the reconciliation between the two theories is not so trivial, both at the mathematical level of carrying out the self-coupling interactions and at the level of interpreting the physical content of the two theories.

Then, I will revisit the recent approaches to the spin-2 field self-coupling derivation of general relativity and analyze what are the crucial steps in it. In particular, I will argue that different authors propose different and conflicting strategies to solve the self-coupling problem as a consequence of the different interpretations and commitments to the physical content of the theories. Starting from this analysis, I will reason on the level of equivalence between the two theories and conclude that the formalisms of spin-2 gravity and general relativity are not translatable into each other without committing in advance to some interpretation. Consequently, I will also conclude that spin-2 gravity and general relativity are theoretically inequivalent.