The mass-zero spin-two field and gravitational theory.

Demonstration that the conventional theory of the mass-zero spin-two field with sources introduces extraneous nonspin-two field components in source regions and fails to be covariant under the full or restricted conformal group. A modified theory is given, expressed in terms of the physical components of mass-zero spin-two field rather than in terms of 'potentials,' which has no extraneous components inside or outside sources, and which is covariant under the full conformal group. For a proper choice of source term, this modified theory has the correct Newtonian limit and automatically implies that a symmetric second-rank source tensor has zero divergence. It is shown that possibly a generally covariant form of the spin-two theory derived here can be constructed to agree with general relativity in all currently accessible experimental situations.