Losing information outside the horizon

TL;DR

This paper explores how information near a black hole horizon becomes inaccessible due to redshift and radiation effects, proposing a universal radius where information is effectively lost, depending on system energy and quantum properties.

Contribution

It introduces a new perspective on information loss near black holes, linking the loss radius to Unruh radiation and system energy gaps, with a universal relation involving BPS states.

Findings

Information is lost near the horizon due to redshift and radiation effects.

The critical radius depends on the system's energy gap and coupling.

For BPS states, the loss radius is the geometric mean of black hole and extremal radii.

Abstract

Suppose we allow a system to fall freely from infinity to a point near (but not beyond) the horizon of a black hole. We note that in a sense the information in the system is already lost to an observer at infinity. Once the system is too close to the horizon it does not have enough energy to send its information back because the information carrying quanta would get redshifted to a point where they get confused with Hawking radiation. If one attempts to turn the infalling system around and bring it back to infinity for observation then it will experience Unruh radiation from the required acceleration. This radiation can excite the bits in the system carrying the information, thus reducing the fidelity of this information. We find the radius where the information is essentially lost in this way, noting that this radius depends on the energy gap (and coupling) of the system. We look for some universality by using the highly degenerate BPS ground states of a quantum gravity theory (string theory) as our information storage device. For such systems one finds that the critical distance to the horizon set by Unruh radiation is the geometric mean of the black hole radius and the radius of the extremal hole with quantum numbers of the BPS bound state. Overall, the results suggest that information in gravity theories should be regarded not as a quantity contained in a system, but in terms of how much of this information is accessible to another observer.