Y. Brihaye et al., Finite energy-action solutions of p(1) Yang-Mills equations on p(2) Schwarzschild and deSitter backgrounds in dimensions d >= 4, J MATH PHYS, 41(8), 2000, pp. 5490-5509
Physically relevant gauge and gravitational theories can be seen as special
members of hierarchies of more elaborate systems. The Yang-Mills (YM) syst
em is the first member of a hierarchy of Lagrangians which we will index by
p(1), and the Einstein-Hilbert (EH) system of general relativity is the fi
rst member of another hierarchy which we index by p(2). In this paper, we s
tudy the classical equations of the p(1)=1,2 YM hierarchy considered in the
background of special geometries (Schwarzschild, deSitter, anti-deSitter)
of the p(2)=1,2,3 EH hierarchy. Solutions are obtained in various dimension
s and lead to several examples of nonself-dual YM fields. When p(1)=p(2) se
lf-dual solutions exist in addition. Their action is equal to the Chern-Pon
tryagin charge and can be compared with that of the nonself-dual solutions.
(C) 2000 American Institute of Physics. [S0022-2488(00)04008-1].