Dark Matter or Additional Gravitational Forces Generated by Non-Spherical Mass Distributions?

Enbang Li

doi:10.1142/s2424942417500049

Abstract

The measured orbital velocity distributions of stars in galaxies and the observed gravitational lensing effects in galaxy clusters suggest that there should be more mass than that can be explained by the visible mass of stars, gas and dust in the galaxies. This unseen mass or matter, generally referred to as dark matter, has puzzled physicists for a few decades and has now become one of the greatest unsolved mysteries in modern science. So far, all of the efforts aiming to generate and detect the exotic dark matter substance have yielded negative results. Here, starting from Newton’s law of gravity, we show that the spherical mass distribution models originally employed for estimating the masses of galaxies could cause the discrepancy between the actual masses and those calculated from the rotational velocities. It is demonstrated that additional gravitational effects are generated from non-spherical mass distributions in the cosmic structures. The currently observed rotation curves and gravitational lensing effects in galaxies and galaxy clusters could be explained under the frameworks of Newtonian gravity and Einstein’s general theory of relativity when proper mass distributions are considered.

Highlights

According to Newton's law of gravity, for a particle of mass m orbiting with velocity v around a spherical distribution of mass M, at distance r from the center, the centrifugal equilibrium condition requires mv2=r 1⁄4 GmM=r2, where G is the Newton's constant of gravitation
The gravitational force calculations presented in this work clearly show that for non-spherical mass distributions, signicant di®erences in gravitation e®ects could be produced in the near- ̄eld
For nonspherical galaxies or galaxy clusters, if the spheroidal model is employed in galactic dynamics to estimate the masses within galaxies, the results could be overestimated and large discrepancies between the actual masses and those calculated from the rotational velocities might be produced

Summary

Introduction

According to Newton's law of gravity, for a particle of mass m orbiting with velocity v around a spherical distribution of mass M, at distance r from the center, the centrifugal equilibrium condition requires mv2=r 1⁄4 GmM=r2, where G is the Newton's constant of gravitation. Like the Milky Way and the Andromeda (M31), instead of this Keplerian declining behavior, concrete measurements of the stars in the. This is an Open Access article published by World Scientic Publishing Company. E. Li galaxy disks have shown that the rotation velocity distributions are almost constant throughout much of the galaxy disks.[1,2] More and more optical and radio observations indicate that all spiral galaxies that so far have been studied commonly possess °at rotation curves.[3,4] This fact leads to a remarkable conclusion: there are missing masses from the galaxies. The observed gravitational lensing e®ects which are caused by the light de°ections predicted by Einstein's general theory of relativity indicate that there must be more masses in the lensing galaxies to account for the observed phenomena.[5,6,7,8]

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Conclusion