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The famous hoop conjecture by Thorne has been claimed to be violated in curved spacetimes coupled to linear electrodynamics. Hod [1] has recently refuted this claim by clarifying the status and validity of the conjecture appropriately interpreting the gravitational mass M. However, it turns out that violations of the conjecture might seemingly occur also in the well known regular curved spacetimes of gravity coupled to nonlinear electrodynamics. Using the interpretation of M in a generic form accommodating nonlinear electrodynamic coupling, we illustrate that the conjecture is not violated even in such curved spacetimes. In the process, we introduce a Hod function summarizing the 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.

On the hoop conjecture in Einstein gravity coupled to nonlinear electrodynamics