从BTZ黑洞到JT引力：岛屿的几何化
From the BTZ black hole to JT gravity: geometrizing the island
摘要：
从三维的角度研究了JT引力场中二维黑洞的蒸发。在庞加莱坐标系中对AdS $_3$进行部分降维，得到一个在JT引力中耦合到“浴缸”的极端二维黑洞：3D时空剩余部分的全息对偶。将BTZ黑洞部分还原，我们得到了有限温度的版本。我们在三维时空中使用测地线计算辐射的熵。然后，我们专注于有限温度的情况下，并通过引入时间依赖性的参数控制减少描述的动态。当我们慢慢移动黑洞和浴槽之间的分界线时，黑洞的能量线性地减少。通过重新调整BTZ参数，我们将其映射到指数蒸发的更规范的图像。最后，研究辐射随时间的熵可以得到佩奇曲线的几何表示。岛屿地区的外观以自然和直观的方式解释。
英文摘要：
We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS$_3$ in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a 'bath': the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.
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