Yang–Mills instantons in the gravitational instanton backgrounds

The simplest and the most straightforward new algorithm for generating solutions to (anti) self-dual Yang–Mills (YM) equation in the typical gravitational instanton backgrounds is proposed. When applied to the Taub-NUT and the Eguchi–Hanson metrics, the two best-known gravitational instantons, the solutions turn out to be the rather exotic type of instanton configurations carrying finite YM action but generally fractional topological charge values.