A Holographic, Hydrodynamic Model of a Schwarzschild Black Hole
Abstract
Schwarzschild (non-rotating and chargeless) black holes are classically understood to be voids of extreme gravitation. In this study, we propose a holographic model for their interiors, envisioning them instead as a hydrodynamic medium. Motivated by the neutrino composition in Hawking radiation (81%), we model the interior as a degenerate fluid, mirrored by the horizon via AdS/CFT duality. A Schwarzschild metric revised with a signum function as the power of the ratio rS/r distinguishes interior linear-well dynamics from exterior Schwarzschild geometry, rimming the horizon with singularity-like gravitational attraction. A Hamiltonian analysis of the total action leads to formulating a Schr\"odinger-like equation, which offers an alternative representation as the contracted Einstein field equations under a holographic-hydrodynamic framework. This eventually yields an equation of state between holographic pressure and black hole mass density: P=/9. Ideal gas analysis reveals a total particle count of 2.8 times the number of horizon quantum areas, with the Fermi energy far exceeding the Hawking thermal energy, ensuring degeneracy. As our discussion, we explore the mass shell free-fall model of a BH with holographic pressure, and dissect the spherical wave solutions to the Schr\"odinger-like equation describing confined interior fields and freely propagating exterior quanta (i.e., Hawking radiation).
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