Evaporating Black Hole Interior and Complexity Evolution

TL;DR

This paper investigates the interior evolution and complexity of an evaporating black hole in JT gravity, revealing a non-monotonic complexity pattern and loss of self-averaging after the Page time.

Contribution

It introduces a model combining JT gravity with an end-of-the-world brane to analyze complexity evolution during black hole evaporation, including non-perturbative effects.

Findings

Complexity peaks at Page time and then decays exponentially.

Fluctuations in interior length grow large after Page time.

Ensemble averaging is dominated by rare configurations at late times.

Abstract

We study the evolution of the interior of an evaporating black hole in a simple model of Jackiw-Teitelboim (JT) gravity with an end-of-the-world (EoW) brane, where evaporation is modeled by entangling the brane's internal states with an auxiliary radiation system. To probe the black hole interior, we consider a geodesic length extracted from a boundary-to-brane two-point function and interpret its renormalised value as a measure of subsystem complexity. Our computation, based on quenched disorder averaging, includes non-perturbative gravitational effects from both spacetime wormholes and replica wormholes, encoding ensemble averaging over the dual random Hamiltonian and brane-state couplings. Unlike non-evaporating black holes where complexity first grows linearly and then plateaus at late times $\sim{\cal O}(e^{S_{\rm BH}})$, we find that complexity evolution of the black hole subsystem in the evaporating case differs drastically, depending nontrivially on the dimension of the emitted radiation Hilbert space. It grows linearly at early times, reaches a maximum at Page time $\sim{\cal O}({S_{\rm BH}})$, and then decays exponentially. We further show that the relative fluctuations of the interior length remain small before the Page time but become of order one and eventually large at later times: this signals a loss of self-averaging, with the ensemble-averaged complexity dominated by rare configurations rather than by typical realisations.