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Renaud Parentani was one of the leading figures in Quantum Field Theory in curved spacetime, in particular concerning its applications to Hawking-like radiation in analogue models. In this paper dedicated to him, we discuss the characteristic features appearing in the correlation functions in an acoustic black hole formed by a Bose–Einstein condensate, considered as signature of the presence of Hawking radiation in this system. 

A method is presented which allows for the numerical computation of the stress-energy tensor for a quantized massless minimally coupled scalar field in the region outside the event horizon of a 4D Schwarzschild black hole that forms from the collapse of a null shell. This method involves taking the difference between the stress-energy tensor for the in state in the collapsing null shell spacetime and that for the Unruh state in Schwarzschild spacetime. The construction of the modes for the {\it in} vacuum state and the Unruh state is discussed. Applying the method, the renormalized stress-energy tensor in the 2D case has been computed numerically and shown to be in agreement with the known analytic solution. In 4D, the presence of an effective potential in the mode equation causes scattering effects that make the the construction of the in modes more complicated. The numerical computation of the in modes in this case is given.