标题： de Sitter-Schwarzschild的宇宙量子态是静态片分区函数 显示英文标题

标题： Cosmological quantum states of de Sitter-Schwarzschild are static patch partition functions

摘要： 我们在四维 de Sitter-Schwarzschild 时空的“宇宙内部”（未来无穷远的过去因果钻石）中求解 Wheeler-DeWitt 方程。 在最小超空间中有由一个常数 $c$ 标记的一组解，该常数与黑洞的质量共轭。 我们提出这些解与一个对偶量子力学理论的配分函数相对应，在其中 $c$ 充当时间的角色。 这个量子力学理论存在于 de Sitter-Schwarzschild 的“静态补丁”的世界管上，配分函数通过演化相应的 Wheeler-DeWitt 波函数穿过宇宙视界来获得，在宇宙视界处度规分量 $g_{tt}$ 发生符号变化。 我们证明了对偶理论具有对称性代数，该代数是庞加莱代数 $\mathfrak{e}(1,1)$ 的中心扩展，并且 de Sitter 黑洞的熵被编码为对背景 $g_{tt}$ 上的对偶配分函数的平均值。 显示英文摘要

摘要： We solve the Wheeler-DeWitt equation in the 'cosmological interior' (the past causal diamond of future infinity) of four dimensional dS-Schwarzschild spacetimes. Within minisuperspace there is a basis of solutions labelled by a constant $c$, conjugate to the mass of the black hole. We propose that these solutions are in correspondence with partition functions of a dual quantum mechanical theory where $c$ plays the role of time. The quantum mechanical theory lives on worldtubes in the 'static patch' of dS-Schwarzschild, and the partition function is obtained by evolving the corresponding Wheeler-DeWitt wavefunction through the cosmological horizon, where a metric component $g_{tt}$ changes sign. We establish that the dual theory admits a symmetry algebra given by a central extension of the Poincar\'e algebra $\mathfrak{e}(1,1)$ and that the entropy of the dS black hole is encoded as an averaging of the dual partition function over the background $g_{tt}$.