On the Relation between Gravitational Field Line Deflection 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 deflection, this paper proposes that this devi-ation originates from the modulation effect of matter spatial configuration on thespatial distribution of gravitational field lines. By establishing a three-point model(gravitational source A, deflection source B, observation point C), this paper de-rives the general expression for the gravitational correction factor Y , proving thatthe gravitational anomaly arises from the deflection of field lines in non-sphericallysymmetric matter distributions, which leads to changes in field line density at theobservation point. This paper further explores the geometric interpretation of ”massas area,” pointing out that in non-spherically symmetric cases, mass alone cannotuniquely determine the gravitational effect, and configuration information is an in-dependent physical degree of freedom. The theory presented in this paper does notrely on dark matter or modified gravity assumptions, extending Newtonian grav-ity from the ”spherically symmetric special case” to the general case of ”arbitraryconfigurations.”