  We study the stress energy two-point function to show how short distance
correlations across the horizon transform into correlations among asymptotic
states, for the Unruh effect, and for black hole radiation. In the first case
the transition is caused by the coupling to accelerated systems. In the second,
the transition is more elusive and due to the change of the geometry from the
near horizon region to the asymptotic one. The gradual transition is
appropriately described by using affine coordinates. We relate this to the
covariant regularization used to evaluate the mean value of the stress energy.
We apply these considerations to analogue black holes, i.e. dispersive
theories. On one hand, the preferred rest frame gives further insight about the
transition, and on the other hand, the dispersion tames the singular behavior
found on the horizon in relativistic theories.
