Relativistic invariant Laplace wave equation used on galaxies

Abstract

In this paper an extended version of a new universal formula of the rotation velocity distribution of galaxies and a new formula of the energy density distribution of galaxies are presented.They are based on a relativistic invariant LaPlace wave equation where it has been possible to obtain expressions for the rotation velocity - and energy density distributions versus distance to the galactic centre. Several mathematical proofs of these new formulas are also given. These formulas are divided into a Keplerian (general relativity)-and a relativistic (special relativity) part. According to the rotation velocity distribution of the galaxies the rotation velocity increases very rapidly from the center and reach a plateau which is constant out to large distance from the centre. This is in accordance with observations and is also in accordance with the main structure of rotation velocity versus distance from different galaxy measurements. It is also possible to determine the mass, radius and maximum rotation velocity of the galaxy from these rotation velocity-and energy density calculations. Computer simulations were also performed to establish and verify the rotation velocity and energy density distributions in the galaxy system, according to this paper. These computer simulations are in accordance with observations in two and three dimensions. It was also possible to study the matching percentage in these calculations showing a very high matching percentage between theoretical and observational values with this new formula. The energy density distributions were also shown of several galaxies together with comparing photos from the space of these galaxies. This comparison gave a very realistic appearance.