# Holographic CFT states for localized perturbations to AdS black holes

## TL;DR

This paper constructs holographic CFT states corresponding to localized scalar perturbations of AdS black holes, exploring how sources can produce localized perturbations near the horizon while maintaining finite amplitudes.

## Contribution

It provides a general map between sources and scalar field perturbations for arbitrary mass and investigates the localization of perturbations in the black hole context.

## Key findings

- Localized perturbations can be generated with small amplitudes.
- Perturbation localization is limited by source divergence constraints.
- The construction applies to scalar fields of arbitrary mass.

## Abstract

In this note, we describe a holographic CFT construction of states dual to scalar perturbations of the maximally extended three-dimensional AdS-Schwarzschild black hole. The states are constructed by adding sources for a scalar operator to the path integral that constructs the thermofield double state. For a scalar field of arbitrary mass, we provide the general map between sources and scalar field perturbations at linear order. With this, we investigate to what extent it is possible using this construction to produce perturbations localized to one side of the black hole horizon. Our results suggest that it is possible to produce arbitrarily localized perturbations (and thus, plausibly, general linear perturbations to the black hole initial data slice), but that the amplitude of the perturbation must be taken small as the perturbation becomes more localized in order that the sources do not diverge, as found for the pure AdS case considered in arXiv:1709.10101.