Scaling arguments and gravitating solitons

Scaling arguments are generalized to discuss the existence and the stability of static, spherically symmetric self-gravitating solitons in asymptotically flat and asymptotically anti-de Sitter spacetimes in $D$ dimensions. The formulas obtained from the scaling arguments are applied to the Einstein–Yang–Mills solitons with higher order terms in $D=4$ and $D=5$ dimensions and the Einstein–Yang–Mills–Chern–Simons solitons in $D=5$ dimension. We have shown that the negative cosmological constant, in general, improves the stability of the solitons. In $D=4$ , in fact, the negative cosmological constant is essential for the stability of the solitons. In $D=5$ , however, the higher order terms or the Chern–Simons term play more crucial role in the stability of the solitons; the possibility of having stable solitons exists in an asymptotically flat spacetime.