On the Cross-Scale Prospects of the Logarithmically Corrected Gravitational Potential: From Black Hole Singularities to Galactic Rotation
Abstract
We derive an effective gravitational potential \( Φ_{halo} (r)∼-[ln( r/r_*)+1]/r \) from the asymptotic behavior of dark matter halo models. At microscopic scales, the logarithmic term changes sign, producing repulsion that prevents matter from collapsing into a singularity. The corresponding logarithmically corrected Schwarzschild metric yields parameter-free, a priori predictions for the shadows of Sgr A* and M87* that agree with Event Horizon Telescope observations. Six falsifiable predictions for unobserved black holes, particularly NGC315, can discriminate this metric from the Kerr solution; we also make falsifiable predictions for the periastron precession of stars S4711 and S4716 based on the same framework (Appendix D). On galactic scales, the same logarithmic term fits rotation curves of the Milky Way, Andromeda, and NGC2974 using only ordinary matter, and passes the Bullet Cluster lensing test. Tidal effects in the Solar System are far below current experimental limits, ensuring consistency with the equivalence principle and parameterized post-Newtonian tests. We further derive the modified field equations via coarse-grained variation (Appendix B) from the effective action of a quantum vortex background, thus providing a more complete theoretical bridge to the modified Poisson equation and metric used in the main text. This effective theoretical framework indicates that various gravitational phenomena from black holes to galaxies may share a common quantum…
Read the paper
Related studies
- A Survey on Knowledge Graphs: Representation, Acquisition, and Applications
- Toxicity of nanomaterials
- The Human Gene Mutation Database: towards a comprehensive repository of inherited mutation data for medical research, genetic diagnosis and next-generation sequencing studies
- Halogen bonding (X‐bonding): A biological perspective
- Biofilm formation at the air–liquid interface by the Pseudomonas fluorescens SBW25 wrinkly spreader requires an acetylated form of cellulose
- Opioid Activation of Toll-Like Receptor 4 Contributes to Drug Reinforcement
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.