  Einstein's equations in a tetrad formulation are derived from a linear theory
in flat spacetime with an asymmetric potential using free field gauge
invariance, local Lorentz invariance and universal coupling. The gravitational
potential can be either covariant or contravariant and of almost any density
weight. These results are adapted to produce universally coupled massive
variants of Einstein's equations, yielding two one-parameter families of
distinct theories with spin 2 and spin 0. The theories derived, upon fixing the
local Lorentz gauge freedom, are seen to be a subset of those found by
Ogievetsky and Polubarinov some time ago using a spin limitation principle. In
view of the stability question for massive gravities, the proven non-necessity
of positive energy for stability in applied mathematics in some contexts is
recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier
than that of the spin 2, as well as lighter than or equal to it, and so provide
phenomenological flexibility that might be of astrophysical or cosmological
use.
