Finite energy / action solutions of p 1 Yang – Mills equations on p 2 Schwarzschild and deSitter backgrounds in dimensions d ≥ 4

Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by p1, and the Einstein-Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by p2. In this paper, we study the classical equations of the p1 = 1, 2 YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter, anti-deSitter) of the p2 = 1, 2, 3 EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of non-self-dual YM fields. When p1 = p2 self-dual solutions exist in addition. Their action is equal to the Chern-Pontryagin charge and can be compared with that of the non-self-dual solutions.