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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19673694 |
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| _version_ | 1866901142701604864 |
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| author | An, Haizhong |
| author_facet | An, Haizhong |
| contents | <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div>We show that a nonlinear scalar field with a Mexican-hat potential, coupled to its own gravitational field, naturally produces an isothermal-sphere density profile <span>ρ(r)∝1/r2</span> in spherical equilibrium—yielding flat galactic rotation curves without invoking dark matter particles or modifications to gravity. The mechanism is a balance between gravitational compression (inward) and the field’s nonlinear restoring pressure (outward), analogous to the thermal-pressure balance in classical isothermal gas spheres but with the scalar field’s self-interaction replacing thermal motion. Numerical simulation of the spherically symmetric time-dependent Ginzburg–Landau equation with gravitational self-feedback confirms that (i) the density power-law index converges to <span>−2.0</span> across the halo region, (ii) the resulting rotation curve is flat to within <span>0.2%</span> variation, and (iii) these results are robust across a factor-of-50 range of the gravitational coupling constant <span>G</span>. At sufficiently large radii the field pressure dominates over gravity and the density returns to the uniform vacuum value, producing a natural Keplerian decline in the outer rotation curve—consistent with recent Gaia DR3 observations of the Milky Way beyond <span>∼16</span> kpc. The model predicts negligible effects at solar-system scales (<span>δρ/ρ0∼10−18</span>), preserving standard Keplerian dynamics. No free parameters are tuned to fit rotation-curve data; the flat profile is a structural inevitability of the self-gravitating nonlinear equilibrium.</div> <div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div> <div> <div> <div> <div> </div> </div> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19673694 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Flat Rotation Curves from Vacuum Pressure in a Self-Gravitating Nonlinear Scalar Field An, Haizhong <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div> <div>We show that a nonlinear scalar field with a Mexican-hat potential, coupled to its own gravitational field, naturally produces an isothermal-sphere density profile <span>ρ(r)∝1/r2</span> in spherical equilibrium—yielding flat galactic rotation curves without invoking dark matter particles or modifications to gravity. The mechanism is a balance between gravitational compression (inward) and the field’s nonlinear restoring pressure (outward), analogous to the thermal-pressure balance in classical isothermal gas spheres but with the scalar field’s self-interaction replacing thermal motion. Numerical simulation of the spherically symmetric time-dependent Ginzburg–Landau equation with gravitational self-feedback confirms that (i) the density power-law index converges to <span>−2.0</span> across the halo region, (ii) the resulting rotation curve is flat to within <span>0.2%</span> variation, and (iii) these results are robust across a factor-of-50 range of the gravitational coupling constant <span>G</span>. At sufficiently large radii the field pressure dominates over gravity and the density returns to the uniform vacuum value, producing a natural Keplerian decline in the outer rotation curve—consistent with recent Gaia DR3 observations of the Milky Way beyond <span>∼16</span> kpc. The model predicts negligible effects at solar-system scales (<span>δρ/ρ0∼10−18</span>), preserving standard Keplerian dynamics. No free parameters are tuned to fit rotation-curve data; the flat profile is a structural inevitability of the self-gravitating nonlinear equilibrium.</div> <div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div> <div> <div> <div> <div> </div> </div> </div> </div> </div> |
| title | Flat Rotation Curves from Vacuum Pressure in a Self-Gravitating Nonlinear Scalar Field |
| url | https://doi.org/10.5281/zenodo.19673694 |