  The total mass, the Witten type gauge conditions and the spectral properties
of the Sen-Witten and the 3-surface twistor operators in closed universes are
investigated. It has been proven that a recently suggested expression ${\tt M}$
for the total mass density of closed universes is vanishing if and only if the
spacetime is flat with toroidal spatial topology; it coincides with the first
eigenvalue of the Sen-Witten operator; and it is vanishing if and only if
Witten's gauge condition admits a non-trivial solution.
  Here we generalize slightly the result above on the zero-mass configurations:
${\tt M}=0$ if and only if the spacetime is holonomically trivial with toroidal
spatial topology. Also, we show that the multiplicity of the eigenvalues of the
(square of the) Sen-Witten operator is at least two, and a potentially viable
gauge condition is suggested. The monotonicity properties of ${\tt M}$ through
the examples of closed Bianchi I and IX cosmological spacetimes are also
discussed. A potential spectral characterization of these cosmological
spacetimes, in terms of the spectrum of the Riemannian Dirac operator and the
Sen-Witten and the 3-surface twistor operators, is also indicated.
