标题： 聚焦与全息假设 显示英文标题

标题： Focusing and the Holographic Hypothesis

摘要： 苏斯金引入的“屏幕映射”用于实现‘t Hooft的全息假设，对此进行了研究。 对于单一的屏幕时间，黑洞事件视界的图像有无穷多个，其中几乎所有图像在屏幕上的面积都小于视界面积。 这是由于焦散点的存在，这与聚焦方程一致。 然而，屏幕过去（或未来）的{\it 边界}遵守面积定理，因此总是给出一个向屏幕扩展的映射，这符合全息假设的要求。 这些考虑通过几个轴对称静态黑洞时空进行了说明。 显示英文摘要

摘要： The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.