The binding of cosmological structures by massless topological defects
Richard Lieu, The binding of cosmological structures by massless topological defects, Monthly Notices of the Royal Astronomical Society, Volume 531, Issue 1, June 2024, Pages 1630–1636, https://doi.org/10.1093/mnras/stae1258
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is mitigated, at least in part.
The nature of dark matter (DM), defined specifically in this letter as an unknown component of the cosmic substratum responsible for the extra gravitational field that binds galaxies and clusters of galaxies, has been an enigma for more than a century since the pioneering papers of Kapteyn ( 1922) and Oort ( 1932), Spitzer observation (Morales-Salgado et al. 2022), and Gaia observation (Battaglia & Nipoti 2022) on galactic scales, and Zwicky ( 1933) and Chaurasiya et al ( 2024) on the scale of clusters. Although the laboratory search for DM is an ongoing effort, see e.g. Aalbers et al ( 2023) and Cebrian ( 2023), alternative theories of gravity were also proposed to enable a considerably smaller amount of matter than is required by Newtonian gravity (and General Relativity in the weak field limit) to produce the same gravitational field strength, see Nojiri et al. ( 2017) and references therein.
