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arXiv · 2402.14235

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

Mengqi Lu·Robert B. Mann
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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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Mengqi Lu, Robert B. Mann. 2024-02-22. Lagrangian partition functions subject to a fixed spatial volume constraint in the Lovelock theory. https://arxiv.org/abs/2402.14235

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