Comments on the non-existence of unified hoop conjecture

Abstract In a recent article, Hod (Eur Phys J C 80:982, 2020) has concluded the non-existence, heretofore unnoticed, of a unified Thorne’s hoop conjecture that holds for the quasi-local mass, $$\mathcal {M}(r\le R_{+})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> for static Reissner–Nordstrőm black hole, but does not hold for the spinning electrically charged Kerr–Newman black holes, when the same quasi-local mass is used. While the conclusion is correct and important, we wish to point out a curious exception for which the conjecture holds in a unified way for both the static and spinning tidal charged 4 d braneworld black holes of string theory, when the mass in the conjecture is the same quasi-local mass.