Gravitation field theory in flat space (in the presence of an electomagnetic field) with the most general stress tensor: equivalence with einstein's theory

Abstract

Gravitational field equations and equations of motion for charged particles are obtained by an interative method, starting from a Lagrangian density in the "unrenormalized" flat space-time. Assuming (a) that the proper masses and charges of the particles are constant and (b) that the gravitational potential is a tensor (no scalar component) in the linearized version (first order in the coupling constant $f$) we obtain, by imposing consistency to all orders in $f$, Einstein's theory which is therefore sounder in the field-theoretic approach than in the usual Riemannian one where there is some arbitrariness (cosmological term, etc). The convergence of our procedure is based on Deser's method but also includes the presence of electromagnetic fields and considers in addition to the energy-momentum tensor ${T}_{\ensuremath{\alpha}\ensuremath{\beta}}$, the most general divergenceless tensor ${t}_{\ensuremath{\alpha}\ensuremath{\beta}}$ depending on four arbitrary parameters which prove to be no longer observable in the "renormalized" space.