Gravity as embedding theory and the distribution of matter in galaxies

TL;DR

This paper explores an embedding theory of gravity in higher-dimensional space, proposing that additional fictitious matter arising from the theory could explain dark matter phenomena in galaxies, with analytical methods to predict density profiles.

Contribution

It introduces a novel embedding gravity framework that yields modified field equations and interprets extra matter as dark matter, providing a new approach to galaxy matter distribution analysis.

Findings

Method to derive matter density profiles near galaxy centers

Ability to distinguish core versus cusp density profiles

Analytical approach based on particle trajectory distribution

Abstract

The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to more general field equations than Einstein's equations. By writing them in the form of Einstein's equations with the contribution of additional fictitious matter, one can try to interpret this matter as dark matter. In order to study the behavior of this fictitious matter near the centers of real galaxies, we discuss an analytical method of obtaining corresponding matter density profiles. This method is based on the consideration of the distribution function of particles over all possible trajectories and allows us to estimate the type (core or cusp) of the emerging density profile.