On Quantum Correlations across the Black Hole Horizon

Inspired by the condensed-matter analogues of black holes, we study the quantum correlations across the event horizon reflecting the entanglement between the outgoing particles of the Hawking radiation and their in-falling partners. For a perfectly covariant theory, the total correlation is conserved in time and piles up arbitrary close to the horizon in the past, where it merges into the singularity of the vacuum two-point function at the light cone. After modifying the dispersion relation (i.e., breaking Lorentz invariance) for large $k$, on the other hand, the light cone is smeared out and the entanglement is not conserved but actually created in a given rate per unit time.