标题： 宇宙学观测站 显示英文标题

标题： Cosmological Observatories

摘要： 我们研究在存在类时边界的情况下，de Sitter 空间的静态区域。 我们在边界处规定诱导度规的共形类和外曲率的迹，$K$是固定的。 我们给出了在这些边界条件下，静态和球对称配置在半经典近似下的 de Sitter 空间的热力学结构。 在三维时空维度中，并且在环面欧几里得边界上$K$为常数时，我们发现对于所有$K$，时空是热稳定的。 在四维时空维度中，热稳定性取决于$K$的值。 已经确定，当$K$足够大时，受共形边界条件限制的 de Sitter 静态区域是热稳定的。 这与包含宇宙视界区域的狄利克雷问题形成对比，该区域具有负比热。 我们分析了在共形边界条件下的线性化爱因斯坦方程。 在类时边界的世界线极限下，底层模式与静态区域的准正则模式相关联。 在类时边界接近宇宙事件视界的情况下，线性化模式被解释为流体动力学系统中的剪切和声波模式。 此外，我们发现了具有正虚频率的模式。 在局部惯性参考系中，并取拉伸宇宙视界极限，这些模式最多以多项式方式增长。 显示英文摘要

摘要： We study the static patch of de Sitter space in the presence of a timelike boundary. We impose that the conformal class of the induced metric and the trace of the extrinsic curvature, $K$, are fixed at the boundary. We present the thermodynamic structure of de Sitter space subject to these boundary conditions, for static and spherically symmetric configurations to leading order in the semiclassical approximation. In three spacetime dimensions, and taking $K$ constant on a toroidal Euclidean boundary, we find that the spacetime is thermally stable for all $K$. In four spacetime dimensions, the thermal stability depends on the value of $K$. It is established that for sufficiently large $K$, the de Sitter static patch subject to conformal boundary conditions is thermally stable. This contrasts the Dirichlet problem for which the region encompassing the cosmological horizon has negative specific heat. We present an analysis of the linearised Einstein equations subject to conformal boundary conditions. In the worldline limit of the timelike boundary, the underlying modes are linked to the quasinormal modes of the static patch. In the limit where the timelike boundary approaches the cosmological event horizon, the linearised modes are interpreted in terms of the shear and sound modes of a fluid dynamical system. Additionally, we find modes with a frequency of positive imaginary part. Measured in a local inertial reference frame, and taking the stretched cosmological horizon limit, these modes grow at most polynomially.