  In abstract Yang-Mills theory the standard instanton construction relies on
the Hodge star having real eigenvalues which makes it inapplicable in the
Lorentzian case. We show that for the affine connection an instanton-type
construction can be carried out in the Lorentzian setting. The Lorentzian
analogue of an instanton is a spacetime whose connection is metric compatible
and Riemann curvature irreducible ("pseudoinstanton"). We suggest a
metric-affine action which is a natural generalization of the Yang-Mills action
and for which pseudoinstantons are stationary points. We show that a spacetime
with a Ricci flat Levi-Civita connection is a pseudoinstanton, so the vacuum
Einstein equation is a special case of our theory. We also find another
pseudoinstanton which is a wave of torsion in Minkowski space. Analysis of the
latter solution indicates the possibility of using it as a model for the
neutrino.
