English

Remove point-mass concept-remove singularities from GR

General Physics 2025-03-26 v3

Abstract

Singularities in Newton's gravitation, in general relativity (GR), in Coulomb's law, and elsewhere in classical physics, stem from two ill conceived assumptions: a) there are point-like entities with finite masses, charges, etc., packed in zero volumes, and b) the non-quantum assumption that these point-likes can be assigned precise coordinates and momenta. In the case of GR, we argue that the classical energy-momentum tensor in Einstein's field equation is that of a collection of point particles and is prone to singularity. In compliance with Heisenberg's uncertainty principle, we suggest to replace each constituent of the gravitating matter with a suitable quantum mechanical equivalent, here a Klien-Gordon (KG) or a Yukawa-ameliorated version of it, YKG field. KG and YKG fields are spatially distributed entities. They do not end up in singular spacetime points nor predict singular blackholes. On the other hand, YKG waves reach infinity as 1re(κ±ik)r\frac{1}{r}e^{-(\kappa\pm i k)r}. They create the Newtonian r2r^{-2} term as well as a non-Newtonian r1r^{-1} force. The latter is capable of explaining the observed flat rotation curves of spiral galaxies, and is interpretable as an alternative gravity, a dark matter scenario, etc. There are ample observational data on flat rotation curves of spiral galaxies, coded in the Tully-Fisher relation, to support our propositions.

Keywords

Cite

@article{arxiv.2404.18954,
  title  = {Remove point-mass concept-remove singularities from GR},
  author = {Yousef Sobouti and Haidar Sheikhahmadi},
  journal= {arXiv preprint arXiv:2404.18954},
  year   = {2025}
}

Comments

18 pages, 3 figures, 1 table

R2 v1 2026-06-28T16:10:13.767Z