The Typical-State Paradox: Diagnosing Horizons with Complexity

TL;DR

This paper introduces a complexity-based diagnostic for black hole horizon transparency, revealing that opaque horizons are unstable and tend to become transparent under perturbations, reconciling contradictory observations.

Contribution

It proposes a novel complexity growth criterion to diagnose horizon transparency and demonstrates the instability of opaque horizons, advancing understanding of black hole horizon dynamics.

Findings

Opaque horizons are highly unstable and become transparent after perturbations.

Computational complexity increases over time for transparent horizons.

Most black holes formed naturally have transparent horizons.

Abstract

The concept of transparent and opaque horizons is defined. One example of opaqueness is the presence of a firewall. Two apparently contradictory statements are reconciled: The overwhelming number of black hole states have opaque horizons; and: All black holes formed by natural processes have transparent horizons. A diagnostic is proposed for transparency, namely that the computational complexity of the state be increasing with time. It is shown that opaque horizons are extremely unstable and that the slightest perturbation will make them transparent within a scrambling time.