论文标题
二维几乎de Sitter重力
Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity
论文作者
论文摘要
我们研究了在Jackiw-teitelboim（JT）重力偶联的二维de Sitter空间（$ \ text {ds} _ {2} $）的半古典热力学（$ \ text {ds} _ {2} $）。我们将布朗和约克的准本地形式延伸到$ \ text {ds} _ {2} $，其中在静态贴片中引入了及时的边界，以唯一定义保守的电荷，包括Quasi-local Energy。边界将静态贴片分为两个系统，一个宇宙系统和一个黑洞系统，前者在热波动下是不稳定的，而后者稳定。衍生出半古典的准局部第一定律，在该法律上，长臂猿熵被广义熵取代。在微域合奏中，广义熵是固定的。此外，我们显示了半古典JT重力中因果钻石的壳欧几里德微域的作用等于减去钻石的广义熵，因此熵的极端化是从最小化作用的情况下。因此，我们为$ u（1）$ symmetric $ \ text {ds} _ {2} $背景提供了岛规则的第一原理推导，而无需调用副本技巧。我们讨论了我们发现对静态贴片的含义。
We study the semi-classical thermodynamics of two-dimensional de Sitter space ($\text{dS}_{2}$) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter. We extend the quasi-local formalism of Brown and York to $\text{dS}_{2}$, where a timelike boundary is introduced in the static patch to uniquely define conserved charges, including quasi-local energy. The boundary divides the static patch into two systems, a cosmological system and a black hole system, the former being unstable under thermal fluctuations while the latter is stable. A semi-classical quasi-local first law is derived, where the Gibbons--Hawking entropy is replaced by the generalized entropy. In the microcanonical ensemble the generalized entropy is stationary. Further, we show the on-shell Euclidean microcanonical action of a causal diamond in semi-classical JT gravity equals minus the generalized entropy of the diamond, hence extremization of the entropy follows from minimizing the action. Thus, we provide a first principles derivation of the island rule for $U(1)$ symmetric $\text{dS}_{2}$ backgrounds, without invoking the replica trick. We discuss the implications of our findings for static patch de Sitter holography.
