Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole

TL;DR

This paper calculates the holographic complexity of an evaporating black hole in a two-dimensional model, revealing new semi-classical features and the relationship between complexity growth and horizon dynamics during evaporation.

Contribution

It introduces a volume-based complexity measure for evaporating black holes in the RST model, capturing semi-classical effects and horizon evolution.

Findings

Complexity growth matches late-time classical behavior.

Early complexity growth occurs around the scrambling time.

Complexity rate tracks the shrinking stretched horizon during evaporation.

Abstract

We obtain the holographic complexity of an evaporating black hole in the semi-classical RST model of two-dimensional dilaton gravity, using a volume prescription that takes into account the higher-dimensional origin of the model. For classical black holes, we recover the expected late time behaviour of the complexity, but new features arise at the semi-classical level. By considering the volume inside the stretched horizon of the evolving black hole, we obtain sensible results for the rate of growth of the complexity, with an early onset of order the black hole scrambling time followed by an extended period where the rate of growth tracks the shrinking area of the stretched horizon as the black hole evaporates.