A Holographic, Hydrodynamic Model of a Schwarzschild Black Hole
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908345659555840 |
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| author | MacKay, Noah M. |
| author_facet | MacKay, Noah M. |
| contents | 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 $r_S/r$ 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 Schrödinger-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: $P=ρ/9$. Ideal gas analysis reveals a total particle count of $\sim2.8$ 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 Schrödinger-like equation describing confined interior fields and freely propagating exterior quanta (i.e., Hawking radiation). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Holographic, Hydrodynamic Model of a Schwarzschild Black Hole MacKay, Noah M. General Physics 81T35, 83C57, 83E05, 85A30 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 $r_S/r$ 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 Schrödinger-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: $P=ρ/9$. Ideal gas analysis reveals a total particle count of $\sim2.8$ 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 Schrödinger-like equation describing confined interior fields and freely propagating exterior quanta (i.e., Hawking radiation). |
| title | A Holographic, Hydrodynamic Model of a Schwarzschild Black Hole |
| topic | General Physics 81T35, 83C57, 83E05, 85A30 |
| url | https://arxiv.org/abs/2505.00732 |