TITLE:
Quantized Horizons and Bright Black Holes: A Proposed Route to Resolving the Information Paradox
AUTHORS:
Espen Gaarder Haug
KEYWORDS:
Black-Hole Information Paradox, Planck Length, Quantized Horizon, Haug-Spavieri Metric, Extremal Reissner-Nordström Geometry, Hawking Radiation, Unitarity, Intrinsic Black-Hole Luminosity, Accretion Disks
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
29,
2026
ABSTRACT: The black-hole information paradox presupposes a causal boundary that permanently prevents information carried by infalling matter from returning to the exterior. We examine an alternative based on the squared factor
f(
r
)=
(
1−
GM/
(
c
2
r
)
)
2
, which appears in extremal Reissner-Nordström geometry and in the minimal Haug-Spavieri metric, together with an equal-factor geometry for which radial null characteristics satisfy
|
dr/
dt
|=c
wherever the metric is nondegenerate. For the associated escape-velocity expression, the value reaches but does not exceed
c
. Following a nested-sphere construction, an interior mass profile
M(
r
)=
c
2
r/G
gives
v
esc
=c
at every interior radius. This profile is interpreted as a saturation condition rather than an independent demonstration of outward causal escape. Haug’s Planck-quantization program gives
GM/
c
2
=N
ℓ
P
and
r
s
=2N
ℓ
P
for
M=N
m
P
. We extend this idea by treating invariant areal radius as a discrete observable and replacing continuum evolution near the nominal horizon with unitary transitions between neighboring radial states. The classical zero of
f(
r
)
then need not correspond to a physical state that permanently divides the Hilbert space. Outgoing massless excitations may pass from interior to exterior states without occupying the degenerate continuum radius, while a minimum radius removes
r=0
from the physical state space. Infalling matter is consequently proposed to be transformed into highly scrambled, information-bearing radiation rather than permanently lost. The framework permits a nonzero intrinsic luminosity in addition to conventional disk and jet emission and suggests observational tests involving delayed radiation, photon-ring structure, polarization correlations, and late-time emission. A complete resolution of the information paradox requires a quantitative transition law, backreaction, entropy evolution, and radiation spectrum, which remain to be developed.