Lecture 20: Nice slices and the Cloning Paradox

After reviewing the Page curve, we discussed the construction of "nice slices." These are Cauchy slices that stay away from the singularity in all regions, and can also be designed to have small extrinsic curvature at all points. Nevertheless, we can use these nice slices to capture the evolution of the black hole geometry all the way from the formation of the black hole to the point where it has substantially evaporated (but remains large in Planck units).

Naively, on these nice slices, we expect quantum gravity corrections to be small. This then leads immediately to, what is called, the "cloning paradox." The Page argument tells us that information exits the black hole after its entropy is half of its original entropy. But then if we consider a nice slice that intersects the infalling matter and also a substantial fraction of the outgoing Hawking radiation, it looks like the same information is present in two places. This apparent conflict with linearity is the cloning paradox.

Lecture 20 notes