  We disclose the behaviour of quantum and classical correlations among all the
different spatial-temporal regions of a space-time with an event horizon,
comparing fermionic with bosonic fields. We show the emergence of conservation
laws for entanglement and classical correlations, pointing out the crucial role
that statistics plays in the information exchange (and more specifically, the
entanglement tradeoff) across horizons. The results obtained here could shed
new light on the problem of information behaviour in non-inertial frames and in
the presence of horizons, giving a better insight about the black hole
information paradox.
