On the Relation between Gravitational Field Line Density Variation and Matter Spatial Configuration – A Modified Gravitational Theory Based on Geometric Principles

Abstract

Newton’s law of universal gravitation has achieved extremely high verificationaccuracy within the solar system scale, and the geometric essence of its inverse-square law is the uniform diffusion of field lines on a spherical surface. However, ongalactic scales, there is a systematic deviation between the observed gravitationaleffects and the gravity expected solely from visible baryonic matter. Starting fromthe geometric principle of field line density variation, this paper proposes that thisdeviation originates from the modulation effect of matter spatial configuration onthe spatial distribution of gravitational field lines. By establishing a three-pointmodel (gravitational source A, deflection source B, observation point C), this paperderives the general expression for the gravitational correction factor Y , provingthat the gravitational anomaly arises from the convergence and divergence of fieldlines in non-spherically symmetric matter distributions – i.e., the redistribution offield line density – which leads to changes in field line density at the observationpoint. This paper further explores the geometric interpretation of ”mass as area,”pointing out that in non-spherically symmetric cases, mass alone cannot uniquelydetermine the gravitational effect, and configuration information is an independentphysical degree of freedom. This paper proposes a general geometric computationalmethod: uniformly divide any three-dimensional matter system into equal-sizedsmall cubes, treat each small cube as an equivalent point mass, and obtain the totalgravitational effect through summation. The theory presented in this paper does notrely on dark matter or modified gravity assumptions, extending Newtonian gravityfrom the ”spherically symmetric special case” to the general case of ”arbitraryconfigurations.”