Black Hole Collapse in the 1/c Expansion

TL;DR

This paper develops a CFT-based framework to analyze black hole formation via matter collapse, demonstrating thermalization and information loss in the 1/c expansion, with results matching gravity calculations.

Contribution

It introduces a continuum Zamolodchikov monodromy method for computing conformal blocks at large central charge, incorporating backreaction effects in collapse scenarios.

Findings

Scalar two-point functions show thermalization at late times

Time-dependent entanglement entropy approaches thermal values

Information loss appears as unitarity violation in 1/c expansion

Abstract

We present a first-principles CFT calculation corresponding to the spherical collapse of a shell of matter in three dimensional quantum gravity. In field theory terms, we describe the equilibration process, from early times to thermalization, of a CFT following a sudden injection of energy at time t=0. By formulating a continuum version of Zamolodchikov's monodromy method to calculate conformal blocks at large central charge c, we give a framework to compute a general class of probe observables in the collapse state, incorporating the full backreaction of matter fields on the dual geometry. This is illustrated by calculating a scalar field two-point function at time-like separation and the time-dependent entanglement entropy of an interval, both showing thermalization at late times. The results are in perfect agreement with previous gravity calculations in the AdS$_3$-Vaidya geometry. Information loss appears in the CFT as an explicit violation of unitarity in the 1/c expansion, restored by nonperturbative corrections.