Yukawa Ameliorated Klein-Gordon approach for resolving GR singularities

• Haidar Sheikhahmadi (School of Astronomy, IPM)

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 replacing 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 $\frac{1}{r}e^{-(k\pm ik)r}$. They create the Newtonian $r^{-2}$ term as well as a non-Newtonian $r^{-1}$ force. The latter can explain 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.