It sounds very strange, since, for instance, the 't Hooft-Polyakov monopole is a solution in flat space and does have a non-zero magnetic charge. The statement that the asymptotic values of the gauge fields are integers  can't be correct, however and the statement about tangential pressure doesn't have anything to do with the issues. The Reissner-Nordstrom black hole is, also, a solution of Einstein's equations that is asymptotically flat and can  have non-zero magnetic charge. And there are many solutions in supergravity.

In the static situation, using Bogomol'nyi type analysis, it can be derived a positive-definite energy functional which has a lower bound. Specializing to the gauge group SU(2) and the t'Hooft-Polyakov ansatz for the gauge and Higgs fields, we seek static, spherically symmetric solutions to the coupled system of equations in both the isotropic and standard coordinate systems. In both cases, in the spontaneously broken symmetry situation, it is found great simplications reducing the solutions of the coupled system to the solution of a single non-linear differential equation, different one in each case, but well-known in other contexts of physics. They found abelian and non-abelian monopole solutions with gravitational fields playing the role of Higgs fields in providing attraction that balances the repulsion due to the gauge fields. Numerical solutions indicate the possibility of blackhole horizons inside the monopoles enclosing the singularity at the origin. Such non-abelian monopoles are then the analogs of Reissner-Nordstr\"om blackholes with magnetic charge.

http://arxiv.org/abs/hep-ph/9310370

Thanks Ali; but I'm not considering monopoles or Higgs fields, just solitons and black holes SU(N) EYM. Possibly I should have been more specific.

Stam: I agree, I mistyped. The magnetic charge takes integer values, not the asymptotic values of the gauge fields.

Stam: In fact, energy density and tangential pressure are central here. See "Local existence proofs for the boundary value problem for static spherically symmetric EYM fields with compact semisimple gauge groups", (2002). There, Kunzle and Oliynyk prove that that energy density and tangential pressure are crucial in the analysis, in that they are the quantities in the Einstein equations that blow up if the asymptotic regularity requirements are not met. It's simple to see once you examine the field equations for a general gauge group.

One last thing Stam: I said 'non-trivial solutions'. The flat space Reissner-Nordstrom solution is an example of a 'trivial' or 'embedded' solution *within* EYM theory. You can tell because it is basically the spherically symmetric Einstein-Maxwell solution, which is Abelian and hence trivial within non-Abelian EYM.