Scaling arguments and gravitating solitons

Abstract

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.