Lagrangian partition functions subject to a fixed spatial volume constraint in the Lovelock theory

• URL: http://arxiv.org/abs/2402.14235v1
• Date: Thu, 22 Feb 2024 02:34:05 GMT
• Title: Lagrangian partition functions subject to a fixed spatial volume constraint in the Lovelock theory
• Authors: Mengqi Lu, Robert B. Mann
• Abstract summary: We evaluate the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of fixed proper volume. We find that there exists sphere saddle metrics for a partition function at a fixed spatial volume in Lovelock theory.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We evaluate the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity [1]. We find that there exists 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 the Bekenstein-Hawking entropy of the boundary area and the one corresponding to a positive effective cosmological constant points to the Wald entropy of the boundary area. We also observe the existence of zeroth order phase transitions between different vacua, a phenomenon distinct from Einstein gravity.

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