标题： 视界之外的有效信息损失 显示英文标题

标题： Effective information loss outside the horizon

摘要： 如果一个系统穿过黑洞视界，那么对无限远处的观察者来说，它的信息就会丢失。 但我们认为，当穿越视界时，{\it 可访问的}的信息会丢失，{\it 前面}时视界被穿越。 黑洞的温度限制了来自已过于接近视界的系统的携带信息的信号。 极端黑洞的温度为 T=0，但在穿越视界前剩下的短时间内，发射一个量子需要最小能量。 如果我们试图将系统带回无限远处进行观测，那么加速辐射会破坏信息。 所有三个考虑因素给出了一个距离视界的关键距离$d\sim \sqrt{r_H\over \Delta E}$，其中$r_H$是视界半径，$\Delta E$是表征系统的能量尺度。 在弦理论中，系统以尽可能密集的方式存储信息，这种加速约束被发现具有几何解释。 这些估计表明，在引力理论中，我们应将信息测量为另一个观察者可以可靠访问的信息量，而不是给定系统内部包含的信息量。 显示英文摘要

摘要： If a system falls through a black hole horizon, then its information is lost to an observer at infinity. But we argue that the {\it accessible} information is lost {\it before} the horizon is crossed. The temperature of the hole limits information carrying signals from a system that has fallen too close to the horizon. Extremal holes have T=0, but there is a minimum energy required to emit a quantum in the short proper time left before the horizon is crossed. If we attempt to bring the system back to infinity for observation, then acceleration radiation destroys the information. All three considerations give a critical distance from the horizon $d\sim \sqrt{r_H\over \Delta E}$, where $r_H$ is the horizon radius and $\Delta E$ is the energy scale characterizing the system. For systems in string theory where we pack information as densely as possible, this acceleration constraint is found to have a geometric interpretation. These estimates suggest that in theories of gravity we should measure information not as a quantity contained inside a given system, but in terms of how much of that information can be reliably accessed by another observer.