时钟只是告诉时间：引力代数在宇宙时空中的实现

我们研究了在半经典量子引力中，针对宇宙背景的观测算子代数，聚焦于两个关键案例：慢滚气动力学和蒸发的 Schwarzschild-de Sitter 黑洞。在这两种情况下，我们 demonstrate 在不引入外部时钟系统或任何渐近引力电荷的情况下，存在非平凡的微分不变观测算子。相反，滚动的气动力学场和蒸发的黑洞 act as physical clocks，allow a definition of gauge-invariant observables at $G = 0$。 resulting algebras are both Type II$_\infty$ factors, but neither is manifestly a crossed product algebra. We establish a connection between the Type II entropy of these algebras and generalized entropies for appropriate states. Our work extends previous results on Type II gravitational algebras and highlights the crucial role of out-of-equilibrium dynamics for defining gauge-invariant observables in semiclassical canonically quantised gravity. We also briefly discuss the construction of gauge-invariant algebras for compact wedges bounded by extremal surfaces in generic spacetimes (i.e. in the absence of any Killing symmetry). In contrast to the inflaton and black hole cases, this algebra does end up being a simple crossed product. No clock or asymptotic charges are required because of the absence of any symmetry in the classical background.