Investigation of the role of conformal covariance in the theory of the mass-zero, spin-two field

The previous work of Coulter on a description of the mass-zero, spin-two field is investigated and extended. Coulter's field equations are first compared with conventional mass-zero, spin-two field equations with sources, and it is found that the conventional theories all have sources with no spin-two content, and acquire extraneous spin components in the region of sources. A conformally covariant representation of the mass-zero, spin-two field in terms of a tensor potential is then given, and a general solution for the tensor potentials obtained in the case of a static, spherically-symmetric source distribution. The extent to which the tensor potential is determined by the field equations is investigated, and it is shown that there is at least one arbitrary function among the components of the potential. A conformally covariant Lagrangian for the mass-zero, spin-two field is written out and equations of motion and conserved quantities for the Lagrangian are calculated. Finally, some comments are offered regarding possible gravitational relevance of this conformally covariant mass-zero, spin-two theory. (Diss. Abstr. Int., B)