Lagrangian partition functions subject to a fixed spatial volume constraint in the Lovelock theory
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.
Keywords
Cite
@article{arxiv.2402.14235,
title = {Lagrangian partition functions subject to a fixed spatial volume constraint in the Lovelock theory},
author = {Mengqi Lu and Robert B. Mann},
journal= {arXiv preprint arXiv:2402.14235},
year = {2024}
}