Recognition: no theorem link
Dyonic black holes supporting nearly-black self-gravitating thin shells
Pith reviewed 2026-05-15 02:20 UTC · model grok-4.3
The pith
Dyonic black holes support self-gravitating nearly-black thin shells at discrete universal radii independent of central mass.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
the discrete radii of these self-gravitating nearly-black Dyson shells are universal in the sense that they are independent of the masses of the central supporting dyonic compact objects.
Load-bearing premise
The dyonic spacetimes of the quasitopological nonlinear electrodynamic field theory possess radial regions satisfying d[r g_tt(r)]/dr → 0^+ that allow static equilibrium for self-gravitating thin shells without violating energy conditions or stability criteria.
read the original abstract
It has recently been revealed that dyonic black-hole spacetimes of a quasitopological non-linear electrodynamic field theory may be characterized by discrete radial regions with the property $dg_{tt}(r)/dr=0$ in which spherically symmetric massive {\it test} shells (Dyson shells with negligible self-gravity) can be supported in static equilibrium states. In the present paper we prove that the dyonic spacetimes of the non-linear electrodynamic field theory may also be characterized by the presence of radial regions with the dimensionless property $d[r\cdot g_{tt}(r)]/dr\to0^+$ in which massive {\it self-gravitating} thin shells that are on the verge of becoming black holes can be supported in static equilibrium states. Intriguingly, it is proved that the discrete radii of these self-gravitating nearly-black Dyson shells are universal in the sense that they are independent of the masses of the central supporting dyonic compact objects.
Editorial analysis
A structured set of objections, weighed in public.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption Dyonic black-hole spacetimes exist in the quasitopological nonlinear electrodynamic field theory with the metric property d[r g_tt(r)]/dr → 0^+ at discrete radii.
- domain assumption Thin-shell approximations remain valid when self-gravity is included and the shell is on the verge of horizon formation.
Reference graph
Works this paper leans on
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[1]
(massive test shells with negligible self-gravity) cannot be supported in static equilibrium states by charged Reissner-Nordstr¨ om black holes [3–7]. Intriguingly, it has recently been revealed [8] that a simple generalization of electromag- netism, referred to as quasitopological non-linear electromagnetic field theory [9] (see also [10–12] and referenc...
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[2]
Chandrasekhar,The Mathematical Theory of Black Holes, (Oxford University Press, New York, 1983)
S. Chandrasekhar,The Mathematical Theory of Black Holes, (Oxford University Press, New York, 1983). 9
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F. J. Dyson, Science131, 1667 (1960)
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See [4–7] and references therein for the physical properties of massive thin shells in curved spacetimes
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W. Israel. Nuovo Cimento B44, 1 (1966)
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V. E. Hubeny, Phys. Rev. D59, 064013 (1999)
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[14]
Note that the gradient relation (2) together with the propertyg tt(r)>0, which characterizes the exterior region of the curved spacetime, imply the inequalitydg tt(r)/dr <0 at the critical equilibrium radiusr=R c eq of a nearly-black self-gravitating thin shell
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[15]
We use natural units in whichG=c= 1
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[16]
C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation(Freeman, San Francisco, 1973)
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S. L. Shapiro and S. A. Teukolsky,Black holes, white dwarfs, and neutron stars: The physics of compact objects(Wiley, New York, 1983)
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[18]
We use the familiar Schwarzschild coordinates{t, r, θ, ϕ}in the line element (4) of the spher- ically symmetric curved spacetime
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[19]
We shall assume the relationsq >0 andp >0 without loss of generality
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[20]
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions(Dover Publications, New York, 1970)
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[21]
Einstein-Yang-Mills Solitons: The Role of Gravity
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[22]
Here ˙R≡dR/dτ, whereτis the proper time along the worldline of the thin massive shell [5]
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[23]
Note that the gradient relationf ′ −(r=r H)≥0 characterizes the outermost horizon of the central black hole, where the equality sign corresponds to an extremal (zero-temperature) 10 black hole
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[24]
Note that the radius-dependent function [R·f −(R) ′ may have degenerate roots
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[25]
Note that the functionF(R;q, p, α 1, α2) has an inflection point atR − ext =R + ext = (4α2p2/3α1)1/4 forα 2 = (α2 1p2 +q 2)2/12α1p2
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[26]
From Eq. (32) one finds that the dyonic black-hole spacetime (5) with the dimensionless physical parameters (31) has an inner horizon which is characterized by the dimensionless relationr in/M ≃0.097
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[27]
Note that the third positive solution of the critical equation (25) is characterized by the dimensionless relationR c eq/rH ≃0.713 and it is therefore located inside the black hole. 11
discussion (0)
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