Scaling arguments for the existence of static, spherically symmetric solutions of self-gravitating systems

Scaling arguments are generalized to a class of self-gravitating matter models with spherically symmetric field configurations. These include the Einstein-Yang-Mills system for any gauge group and also the Einstein-sigma model, without or with an additional Skyrme term. For the considered class it is possible to express the Schwarzschild mass as a relatively simple nonlocal functional of the matter variables alone. The behaviour of this functional with respect to scaling transformations leads to interesting consequences. In some cases the authors can exclude particle-like solutions, whereas for other models they find some virial relations including gravity. The method is also extended to black holes. As an application they give some necessary existence conditions for solutions of various matter models on a fixed black hole background. Finally they apply the arguments to self-coupled black hole solutions.