Evaporating Black Hole Interior and Complexity Evolution
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, for which complexity first grows linearly and then plateaus at late times ∼cal O(eSBH), 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 shortly before the Page-time crossover ∼cal O(SBH), 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.
Related
- Unitary evolution of an evaporating black hole in canonical quantum gravity
- Matrix scattering and the black hole interior
- Simulating Black Hole Thermality and Interior Scrambling on a Superconducting Quantum Processor
- Black hole interior and time-like entanglement entropy
- Algebraic Complexity and Black Hole Complementarity
BibTeX
@misc{bragagnolo2026evaporating,
title = {{Evaporating Black Hole Interior and Complexity Evolution}},
author = {Nicolò Bragagnolo and S. Prem Kumar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.16619},
eprint = {2605.16619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16619},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evaporating Black Hole Interior and Complexity Evolution
AU - Nicolò Bragagnolo
AU - S. Prem Kumar
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2605.16619
UR - https://arxiv.org/abs/2605.16619
AB - 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, for which complexity first grows linearly and then plateaus at late times ∼cal O(e^S_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 shortly before the Page-time crossover ∼cal O(S_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.
ER -