IJPAM: Volume 35, No. 3 (2007)
ON ONE MINKOWSKI DOMAIN
Providence, Rhode Island, 02918, USA
Abstract.This paper introduces the idea of a ``combined manifold'', which essentially is the graph of a diffeomorphism from one manifold to another. Following a previously published work by the author, this present article addresses a combined space-time 4-manifold by introducing ``combined particles'' , where and separately establish their own distinct 4-manifolds following General Relativity; this is made possible by assuming that only exert gravitational forces. We have proved that this combined 4-manifold is unique thanks to a distinct weighted average of the two metrics from a pair of sets of Einstein Field Equations, with the weights determined by two gravitational constants. As an illustration, we have decomposed the recognized gravitational constant and the Earth mass, and as a motivation, we tender the particle-wave duality as a theoretical support of our hypothetical combined 4-manifold.
Received: January 25, 2006
AMS Subject Classification: 83C05, 53C50, 53C15, 85A40
Key Words and Phrases: Einstein field equations, dark matter, 4-manifold, diagonal map, space-time geometry
Source: International Journal of Pure and Applied Mathematics