Corral, CristóbalGiribet, GastónOlea, Rodrigo2022-05-052022-05-052021-09Physical Review DOpen AccessVolume 104, Issue 615 September 2021 Article number 0640262470-0010https://repositorio.unab.cl/xmlui/handle/ria/22467Indexación: ScopusWe study non-Einstein Bach-flat gravitational instanton solutions that can be regarded as the generalization of the Taub-NUT/bolt and Eguchi-Hanson solutions of Einstein gravity to conformal gravity. These solutions include non-Einstein spaces which are either asymptotically locally flat spacetimes or asymptotically locally anti-de Sitter (AlAdS). Nevertheless, solutions with different asymptotic conditions exist: we find geometries that present a weakened AlAdS asymptotia, exhibiting the typical low decaying mode of conformal gravity. This permits us to identify the simple Neumann boundary condition that, as it happens in the asymptotically AdS sector, selects the Einstein solution out of the solutions of conformal gravity. All the geometries present nonvanishing Hirzebruch signature and Euler characteristic, being single-centered instantons. We compute the topological charges as well as the Noether charges of the Taub-NUT/bolt and Eguchi-Hanson spacetimes, which happen to be finite. This enables us to study the thermodynamic properties of these geometries. © 2021 authors. Published by the American Physical Society.enAlAdS asymptotiaTaub-NUT/bolt and Eguchi-Hanson spacetimes,Bach-flat gravitational instanton solutionsArtículoAtribución 4.0 Internacional (CC BY 4.0)10.1103/PhysRevD.104.064026