New Theory of Gravitation

A locally Lorentz-invariant curved-space theory of gravitation where the local field is a massless, spin-2 field ${{\ensuremath{\phi}}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}$ of Pauli-Fierz type is presented. In this theory ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ is no longer the gravitational potential itself but reduces to a functional ${g}_{\ensuremath{\mu}\ensuremath{\nu}}({{\ensuremath{\phi}}_{\ensuremath{\alpha}}}^{\ensuremath{\beta}})$ of ${{\ensuremath{\phi}}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}$. Several rigorous and a general iteration solution of this type are exhibited. The static central body problem reduces exactly to author's 1958 theory in the special case ${{\ensuremath{\phi}}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}\ensuremath{\rightarrow}{{\ensuremath{\phi}}_{0}}^{0}=\ensuremath{\phi}$ and ${\ensuremath{\partial}}^{\ensuremath{\mu}}{{\ensuremath{\phi}}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}\ensuremath{\rightarrow}{\ensuremath{\partial}}^{0}\ensuremath{\phi}=0$ so that as in that theory the three crucial tests are satisfied.

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