An infalling observer and behind the horizon cutoff

Abstract

Using Papadodimas and Raju construction of operators describing the interior of a black hole, we present a general relation between partition functions of operators describing inside and outside the black hole horizon. In particular for an eternal black hole the partition function of the interior modes may be given in terms those partition functions associated with the modes of left and right exteriors. By making use of this relation we observe that setting a finite UV cutoff will enforce us to have a cutoff behind the horizon whose value is fixed by the UV cutoff. The resultant cutoff is in agreement with what obtained in the context of holographic complexity.

Complexity as a holographic probe of strong cosmic censorship

“…This relation is identical to the one obtained by demanding the saturation of Lloyd's bound in (3.13). This matching is very much reminiscent of the chargeless case already noted in [27]. The charged scenario, in presence of the inner horizon will provide a new interpretation of this result.…”

“…Using this approach for neutral, eternal black holes one may find an expression for the cutoff behind the horizon which is the same as that obtained in the context of holographic complexity [27]. The aim of this section is to extend this study to charged black branes.…”

“…This study follows directly from the construction of interior operators in terms of those describing the exterior regions proposed in [5]. Actually based on this fact one can argue that the partition function of the operators describing the interior of an eternal black hole is proportional to the product of partition functions of operators describing the left and right exteriors of the black hole [27]. At leading order this connection may be reduced to a relation between the on-shell actions evaluated on the inside and outside of the black hole.…”

“…Following [27], let us define the restricted partition function in which the integration is taken over the fields associated with regions I, II or III of the corresponding eternal black hole…”

“…By relating the partition functions inside and outside of the horizon of an eternal black hole using the "mirror operator" construction of Papadodimas and Raju [5,6], the authors of [27] established that a cutoff at a finite radial distance does indeed imply a cutoff behind the horizon. This guarantees a bulk effective field theory at leading order in the 1 N expansion.…”