Gravitational instantons with conformally coupled scalar fields

We present novel regular Euclidean solutions to General Relativity in presence of Maxwell and conformally coupled scalar fields. In particular, we consider metrics the Eguchi-Hanson Taub-NUT families solve field equations analytically. The have nontrivial topology labeled by Hirzebruch signature Euler characteristic that compute explicitly. find that, although are locally inequivalent with original (anti-)self-dual metric, their asymptotically limit leads same global properties. revisit solution previously found literature, analyze nuts bolts structure, obtain renormalized on-shell action as well topological invariants. Additionally, discuss how get modified higher-curvature corrections respect conformal invariance. invariant case, demonstrate both Noether-Wald charges finite without any reference intrinsic boundary counterterms.