Letter: Gravitational Entropy of Constrained Instanton

The seeds for quantum creations of universes areconstrained gravitational instantons. For all compactconstrained instantons with a U(1) isometry, the period of the group parameter is identifiedas the reciprocal of the temperature. If remains a free parameter under the constraints, then theEuclidean action becomes the negative of the entropy. Asexamples, we perform the calculations forthe Taub-nut and Taub-Bolt-type models andstudy the quantum creation of the Taub-nutuniverse.