2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36382The seeds for quantum creations of universes are constrained gravitational instantons. For all compact constrained instantons with U(1) isometry, the period $β$ of the group parameter $τ$ is identified as the reciprocal of the temperature. If $β$ remains a free parameter under the constraints, then the Euclidean action becomes the negative of the "entropy". As examples, we perform the calculations for the Taub-NUT and Taub-bolt-type models and study the quantum creation of the Taub-NUT universe.8 pagesGeneral Relativity and Quantum Cosmologytext