Computational Complexity and Black Hole Horizons

TL;DR

This paper explores the role of computational complexity in black hole physics, particularly in firewall formation, highlighting the difficulty of creating firewalls in certain black hole scenarios and potential implications for understanding black hole horizons.

Contribution

It connects computational complexity with black hole horizon properties, analyzing firewall formation difficulty and suggesting gravity may help study complexity ranges.

Findings

Creating firewalls is extremely difficult for black holes formed by sudden collapse.

Firewalls may become common after exponential time if radiation is contained.

Gravity could provide tools to study complexity between scrambling and exponential growth.

Abstract

Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that while creating firewalls is possible, it is extremely difficult and probably impossible for black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity.