  We investigate, within the framework of Quantum Field Theory in curved space,
the correlations across the horizon of a black hole in order to highlight the
particle-partner pair creation mechanism at the origin of Hawking radiation.
The analysis concerns both acoustic black holes, formed by Bose-Einstein
condensates, and gravitational black holes. More precisely, we have considered
a typical acoustic black hole metric with two asymptotic homogeneous regions
and the Schwarzschild metric as describing a gravitational black hole. By
considering equal time correlation functions, we find a striking disagreement
between the two cases: the expected characteristic peak centered along the
trajectories of the Hawking particles and their partners seems to appear only
for the acoustic black hole and not for the gravitational Schwarzschild one.
The reason for that is the existence of a 'quantum atmosphere' displaced from
the horizon as the locus of origin of Hawking radiation together, and this is
the crucial aspect, with the presence of a central singularity in the
gravitational case swallowing everything is trapped inside the horizon.
Correlations however are not absent in the gravitational case: to see them one
has simply to consider correlation functions at unequal times which indeed
display the expected peak.
