Lecture 2: Entangled modes across null surfaces
We showed that in a quantum field theory in curved spacetime, in the vicinity of any null surface, it is possible to extract degrees of freedom that are entangled in a very specific manner. These degrees of freedom are obtained by integrating the field with a carefully chosen smearing function. Although the intermediate steps required careful calculations, we obtained a simple and beautiful final answer.
In a spacetime with spherical symmetry, it is possible to generalize this construction and obtained entangled modes that are labeled by a spherical harmonic rather than a point.
The correlations that we explored are rather special. They tell us that the state obtained by acting with modes from one side of the null surface is parallel to the state obtained by acting with modes from the other side.
