| _version_ | 1866901315625418752 |
|---|---|
| author | Pray, Matthew |
| author_facet | Pray, Matthew |
| contents | <p>We extend the Grand Relativity (GRL) framework by deriving the modified Tolman-Oppenheimer-Volkoff (TOV) equations that govern hydrostatic equilibrium in the presence of a dynamical scalar field. We demonstrate that the coordinated scaling of fundamental constants (c ∝ ϕ, G ∝ ϕ2, m ∝ ϕ−2) produces a geometric pressure barrier that prevents gravitational collapse to infinite density. The scalar field gradient generates an effective repulsive force scaling as ϕ−3, which dominates over gravity as ϕ → 0. This mechanism creates a ‘Planck Floor’—a minimum physical scale where the<br>locally-measured Planck length grows to meet the shrinking matter distribution, halting collapse at finite physical density. We find the core stabilizes at a physical size of L ∼ 10−24 m (approximately 1011 times the fundamental Planck length), corresponding to extreme coordinate radii in the Einstein frame. The Planck Floor scale follows LPlanck ∝ M 1/3, making it significantly larger than the fundamental Planck scale for astrophysical black holes. We show that the event horizon (rs ∼ 3 km) and physical core are fundamentally decoupled through ϕ-dependent scaling, resolving the classical singularity problem through field dynamics rather than quantum effects. The framework suggests black holes contain frozen, finite-density cores rather than singularities.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19243246 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Singularity Avoidance in Grand Relativity: Modified TOV Equations and the Planck Floor Mechanism Pray, Matthew <p>We extend the Grand Relativity (GRL) framework by deriving the modified Tolman-Oppenheimer-Volkoff (TOV) equations that govern hydrostatic equilibrium in the presence of a dynamical scalar field. We demonstrate that the coordinated scaling of fundamental constants (c ∝ ϕ, G ∝ ϕ2, m ∝ ϕ−2) produces a geometric pressure barrier that prevents gravitational collapse to infinite density. The scalar field gradient generates an effective repulsive force scaling as ϕ−3, which dominates over gravity as ϕ → 0. This mechanism creates a ‘Planck Floor’—a minimum physical scale where the<br>locally-measured Planck length grows to meet the shrinking matter distribution, halting collapse at finite physical density. We find the core stabilizes at a physical size of L ∼ 10−24 m (approximately 1011 times the fundamental Planck length), corresponding to extreme coordinate radii in the Einstein frame. The Planck Floor scale follows LPlanck ∝ M 1/3, making it significantly larger than the fundamental Planck scale for astrophysical black holes. We show that the event horizon (rs ∼ 3 km) and physical core are fundamentally decoupled through ϕ-dependent scaling, resolving the classical singularity problem through field dynamics rather than quantum effects. The framework suggests black holes contain frozen, finite-density cores rather than singularities.</p> |
| title | Singularity Avoidance in Grand Relativity: Modified TOV Equations and the Planck Floor Mechanism |
| url | https://doi.org/10.5281/zenodo.19243246 |