Holographic Banners

TL;DR

This paper introduces the concept of a holographic banner, a function encoding interior black hole states from boundary data, and explores its implications for quantum cosmology and chaotic dynamics inside AdS black holes.

Contribution

It defines and computes the holographic banner for scalar fields in AdS black holes, linking boundary data to interior quantum states and chaotic BKL dynamics.

Findings

Explicit computation of the holographic banner for scalar fields in AdS black holes

Construction of semiclassical states in the black hole interior from boundary data

Proposal of a map from boundary data to near-singularity quantum cosmology

Abstract

This paper is concerned with eternal AdS black holes. The quantum cosmological future and past interior states of the black hole may be placed on an equal footing to the left and right AdS boundary data by considering the on-shell bulk action as a function of the left/right/future/past data: $S[\phi^{(0)L},\phi^{(0)R},\phi^{(0)F},\phi^{(0)P}]$. We call this object a holographic banner, and it obeys the Hamilton-Jacobi equation with respect to all four of its arguments. We compute the holographic banner for a scalar field in an AdS black hole background explicitly and use it to construct the semiclassical state in the future interior obtained from a thermofield double state in the past evolved by arbitrary time- and space-dependent boundary sources. When the spacetime itself is dynamical we explain how the holographic banner gives, in principle, a map from boundary data to near-singularity semiclassical quantum cosmology following chaotic BKL dynamics. We obtain the timescale for the BKL dynamics to ergodically mix the future interior quantum state, given a quantum variance in the past state or a classical ensemble of boundary theories.