On the Hoop conjecture in Einstein gravity coupled to nonlinear electrodynamics

TL;DR

This paper investigates the validity of the hoop conjecture in Einstein gravity coupled with nonlinear electrodynamics, demonstrating that the conjecture holds even in complex curved spacetimes with nonlinear electromagnetic fields.

Contribution

It extends the analysis of the hoop conjecture to nonlinear electrodynamic couplings, showing it is not violated in such curved spacetimes, unlike previous claims.

Findings

The hoop conjecture remains valid in nonlinear electrodynamic curved spacetimes.

A Hod function effectively summarizes the transition between horizon and no horizon regimes.

The interpretation of gravitational mass M is crucial in assessing the conjecture's validity.

Abstract

The famous hoop conjecture by Thorne has been claimed to be\ violated in curved spacetimes coupled to linear electrodynamics. Hod \cite{Hod:2018} has recently refuted this claim by clarifying the status and validity of the conjecture appropriately interpreting the gravitational mass parameter $M$. However, it turns out that partial violations of the conjecture might seemingly occur also in the well known regular curved spacetimes of gravity coupled to \textit{nonlinear electrodynamic}s. Using the interpretation of $M$ in a generic form accommodating nonlinear electrodynamic coupling, we illustrate a novel extension that the hoop conjecture is \textit{not} violated even in such curved spacetimes. We introduce a Hod function summarizing the hoop conjecture and find that it surprisingly encapsulates the transition regimes between "horizon and no horizon" across the critical values determined essentially by the concerned curved geometries.