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I understand that to obtain retarded Green's function using AdS/CFT one needs to put ingoing wave boundary condition at the horizon, when one is considering a finite temperature system.

For system at zero temperature there is no black hole in the AdS. Still people use ingoing wave boundary condition (or pick the solution of the corresponding Euclidean equation of motion which is regular everywhere in the interior and analytically continue that solution to get the solution to the original Minkowski problem.).

My question is following. Suppose I have a geometry (i.e, a metric) that solves Einstein's equations with negative cosmological constant. It is asymptotically AdS but not a black hole. Now it may allow solutions to the EOM for the field which are both regular in the interior (for the Euclidean case, say). In this situation what will be the natural boundary condition to obtain retarded Green's function?

EDIT : I have a silly confusion about regularity. To be regular should a function must vanish at the "centre" of the space? Or it can take only finite values in the interior and may not vanish at the "centre"..

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