Identifying Theoretical Gaps in Hawking's Black Hole Radiation Model in Light of Modern Photonics and Higher-Dimensional Photon Propagation : Photon-Coupled Soft Hair and Higher-Dimensional Photon Channels A Critical Extension of the Soft-Hair Formalism

 Stephen Hawking’s seminal work on black hole thermodynamics and the associated
 Hawking radiation revolutionized our understanding of quantum effects in strong gravita
tional fields. His mathematical framework—melding quantum field theory with general
 relativity—predicted that black holes are not entirely black, but emit thermal radiation due
 to quantum fluctuations near the event horizon.
 The elegance of Hawking’s derivation lies in its use of semi-classical approximations,
 where spacetime curvature is treated classically while quantum effects are applied to matter
 fields. This led to the now-famous prediction that black holes evaporate over time.
 However, this approach inherently assumes a background structure in which photon
 propagation is constrained to classical 3+1 spacetime, with no explicit treatment of how
 photons might behave in variable refractive-index conditions or higher-dimensional manifolds
 predicted by modern photonics research. Such constraints may oversimplify photon-gravity
 interactions, neglecting the possibility that event-horizon-localized photons could experience
 dispersion or modified group velocities if the surrounding vacuum behaves as a structured
 medium—something now increasingly supported by analog gravity experiments and photonic
 crystal studies.
 This paper will reexamine Hawking’s framework by incorporating photonic propagation
 models drawn from modern optical physics, extended to higher-dimensional scenarios. In
 doing so, we identify a subtle but critical theoretical gap that emerges when photons are
 treated not as free particles in a fixed background, but as excitations interacting with
 geometry-dependent refractive structures in both real and extra dimensions. We present an
 extended covariant-phase-space analysis of “soft hair” charges on black hole horizons that
 explicitly includes electromagnetic (photon) degrees of freedom and their higher-dimensional
 propagation channels. Building on the Virasoro-based construction of horizon charges for
 Kerr black holes, we derive electromagnetic surface contributions to the Wald–Zoupas charges
 and compute their effect on central extensions entering the Cardy counting. We show, by
 analytic derivation, that (i) soft photon boundary terms generically modify the horizon
 charge algebra, (ii) in spacetimes with extra spatial dimensions the density of photon soft
 channels grows with the number of transverse dimensions and thus can produce parametrically
 enhanced corrections to the effective central charge, and (iii) these corrections yield concrete,
 computable shifts in the predicted entropy when Cardy-type formulae are applied. The main
 result is an explicit expression for the electromagnetic correction to the central extension
 and the associated entropy correction; we conclude with an assessment of regimes where the
 original gravitational-only treatment undercounts horizon microstates.