Self-dual gravitational instantons in conformal gravity: Conserved charges and thermodynamics

Cristóbal Corral, Gastón Giribet, Rodrigo Olea

Research output: Contribution to journalArticlepeer-review


We 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.

Original languageEnglish
Article number064026
JournalPhysical Review D
Issue number6
Publication statusPublished - 15 Sep 2021

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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