Dr. Abhishek Majhi

Einsteinian gravity, of which Newtonian gravity is a part, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose (Nobel 2020 for the latter). Alongside the axioms of geometry, the hypothesis that forms the basis of both Einsteinian and Newtonian theories of gravity is that bodies with unequal magnitudes of masses fall with the same acceleration under the gravity of a source object. Since, Einstein's equations are one of the assumptions that underlies the proof of the singularity theorem, therefore, the above hypothesis is implicitly one of the founding pillars of the same. In this work, I demonstrate how one can possibly write a non-singular theory of gravity by refining the first axiom of geometry concerning ``a point'', which manifests that the above mentioned hypothesis is only valid in an approximate sense in the ``large distance'' scenario. To mention a specific instance, under the gravity of the earth, a 5 kg and a 500 kg fall with accelerations which differ by approximately 113.148 x 10^(-32) meter/sec^2 and the more massive object falls with less acceleration. Further, I demonstrate why the concept of gravitational field is not definable in the ``small distance'' regime which automatically justifies why the Einstein's and Newton's theories fail to provide any ``small distance'' analysis. I provide a glimpse of what I call ``non-standard physics'' where the concept of ``point mass'' differs from the standard physics literature owing to the refinement of the first axiom of geometry.