Lagrangian Partition Functions Subject to a Fixed Spatial Volume Constraint in the Lovelock Theory

We evaluate here the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of a fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity. It is found that there are sphere saddle metrics for...

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Bibliographic Details
Published inEntropy (Basel, Switzerland) Vol. 26; no. 4; p. 291
Main Authors Lu, Mengqi, Mann, Robert B.
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 01.04.2024
Subjects
Black holes
Cosmological constant
cosmological entropy
de Sitter
Entropy
Euclidean space
gravitational Hilbert space
Hilbert space
Lagrange multiplier
Lovelock gravity
Partitions (mathematics)
Phase transitions
Quantum gravity
Spacetime
Canada
de Sitter
gravitational Hilbert space
Lovelock gravity
cosmological entropy
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Summary:We evaluate here the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of a fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity. It is found that there are sphere saddle metrics for a partition function at a fixed spatial volume in Lovelock theory. Those stationary points take exactly the same forms as in Einstein gravity. The logarithm of Z corresponding to a zero effective cosmological constant indicates that the Bekenstein–Hawking entropy of the boundary area and that corresponding to a positive effective cosmological constant points to the Wald entropy of the boundary area. We also show the existence of zeroth-order phase transitions between different vacua, a phenomenon distinct from Einstein gravity.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e26040291