Effective information loss outside the horizon

TL;DR

This paper argues that information about a system falling into a black hole becomes inaccessible before crossing the horizon due to temperature limits and acceleration radiation, redefining how information is measured in gravitational systems.

Contribution

It introduces a new perspective on information loss, emphasizing accessible information outside the horizon rather than inside, with a geometric interpretation in string theory.

Findings

Accessible information is lost at a critical distance from the horizon.

Acceleration radiation destroys information during return to infinity.

The critical distance scales as rom the horizon depending on energy.

Abstract

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.