  The black hole information paradox is a contradiction between fundamental
principles which has puzzled physicists for over forty years. The crux of the
problem lies in an assumption about the structure of entanglement across the
event horizon, namely, that the Hilbert space factorizes. While valid in
quantum mechanics, this fails drastically in quantum field theory, and hence a
deeper understanding of entanglement is required if further progress is to be
made. Recently, ideas from algebraic quantum field theory have provided new
insight into this issue, and show promise for elucidating the connection
between entropy and horizons that underlies black hole thermodynamics.
