Quantum correlations through event horizons: Fermionic versus bosonic entanglement

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.