Black Hole Formation in Fuzzy Sphere Collapse

TL;DR

This paper investigates the collapse of a fuzzy sphere of D0-branes in the BFSS model, revealing a transition from classical behavior to black hole formation as initial radius decreases, with open string production playing a key role.

Contribution

It provides a detailed analysis of fuzzy sphere collapse dynamics, identifying the conditions leading to black hole formation and connecting to the Horowitz-Polchinski correspondence point.

Findings

Large initial radius: sphere behaves classically with negligible open string production.

Intermediate radius: open string back-reaction affects dynamics but retains sphere identity.

Small initial radius: sphere collapses into a black hole, crossing the correspondence point.

Abstract

We study the collapse of a fuzzy sphere, that is a spherical membrane built out of D0-branes, in the BFSS model. At weak coupling, as the sphere shrinks, open strings are produced. If the initial radius is large then open string production is not important and the sphere behaves classically. At intermediate initial radius the back-reaction from open string production is important but the fuzzy sphere retains its identity. At small initial radius the sphere collapses to form a black hole. The crossover between the later two regimes is smooth and occurs at the correspondence point of Horowitz and Polchinski.