Analog charged black hole formation via percolation: Exploring cosmic censorship and Hoop conjecture

TL;DR

This paper presents an analog model of charged black hole formation using classical percolation, demonstrating how energy growth and cluster expansion indicate horizon formation and support cosmic censorship, with implications for quantum gravity insights.

Contribution

It introduces a novel percolation-based analog system for black hole formation, linking geometric and energetic criteria, and explores implications for cosmic censorship and quantum extensions.

Findings

Energy and cluster growth are key indicators of black hole formation.

Geometric hoop criteria are necessary but not sufficient for horizons.

Numerical simulations agree with analytical predictions in the continuum limit.

Abstract

We investigate an analog model of charged black hole (BH) formation using the framework of classical percolation. By analyzing the scaling behavior of key quantities, including surface gravity and Komar mass, we establish a robust correspondence between this analog system and gravitational collapse in general relativity. Our numerical simulations of the lattice model show excellent agreement with analytical predictions for the continuum limit, highlighting the potential of analog systems to capture essential features of BH physics. Interestingly, we find that while geometric criteria related to the hoop conjecture are necessary, they are not sufficient for BH formation in our model. Instead, the exponential growth of energy and cluster size emerges as the key indicator, suggesting a novel interpretation of the hoop conjecture and providing further support for cosmic censorship within our analog framework by ensuring horizon formation. This work offers a fresh perspective on the organization of matter within BH event horizons and lays the groundwork for future quantum extensions that could shed light on Hawking radiation and the BH information paradox by linking entanglement entropy in quantum percolation models to BH entropy.