TITLE:
Atomization Theorems in Mathematical Physics and General Relativity
AUTHORS:
Sergei Yurievich Eremenko
KEYWORDS:
Atomic Function, AString, Splines, Series, Spacetime, General Relativity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.1,
January
30,
2023
ABSTRACT: Formulated Atomization Theorems extend the theory of Atomic AString Functions evolving since the 1970s allowing representation of polynomials, complex analytic functions, and solutions of linear and nonlinear differential equations via Atomic Series over smooth finite Atomic Splines. Noting the preservation of analyticity for Ricci and Einstein tensors, special new theorems are formulated for General Relativity representing spacetime field via superpositions of flexible finite “solitonic atoms” resembling quanta. The novel Atomic Spacetime model correlates with A. Einstein’s 1933 paper predicting a new “atomic theory”. The theorems can be applied to many theories of mathematical physics, elasticity, hydrodynamics, soliton, and field theories for unified representation of fields via series over finite Atomic AString Functions which may offer a unified theory under research where fields are connected with a common mathematical ancestor.