Nonexistence theorems for Yang-Mills fields outside the black hole of the Schwarzschild spacetime (Q1263824)

It is proved that a regular static solution of the Yang-Mills equation (not necessarily \(\pm\) self-dual) with a slowly diverging \(L^ 2\)-norm defined with respect to the Schwarzschild metric is trivial (i.e. flat), provided that an appropriate boundary condition at the Schwarzschild radius is satisfied.