Interacting field of spin 2 and the einstein equations
Abstract
The possible local theories of an interacting symmetric tensor field h_{μν} are considered, in which the equations of motion are compatible with a general HilbertLorentz type condition to exclude spin 1. It is shown that in the case of massless tensor field there exists only one such a theory under the assumption of minimal interactions, and the equations of motion coincide exactly with the Einstein equations including all nonlinearities of the latter (1). That is, the field theoretical derivation of the Einstein equations is given. In this approach spacetime remains flat and the nonlinearities peculiar to the Einstein theory are generated by the requirement for interacting gravitons to have spin 2 but not spin 1. As to the massless field this requirement is guarranteed by an invariance under gauge transformations, which on the one hand are analogous to the gauge transformations in electrodynamics and on the other hand are formally equivalent to the general covariant transformations. The generalization of the Einstein equations to the case of a massive tensor field is obtained. Mass terms violate the general covariance and the equivalence principle but the equality of inertial and "gravitational" masses remains valid.
 Publication:

Annals of Physics
 Pub Date:
 November 1965
 DOI:
 10.1016/00034916(65)900771
 Bibcode:
 1965AnPhy..35..167O