# Extrasolar scale change in Newton's Law from 5D `plain' R^2-gravity

## TL;DR

This paper proposes a 5D gravity model based on R^2 gravity without a Lagrangian, suggesting a scale-dependent change in Newton's law from inverse-square to inverse distance at galactic scales, potentially explaining dark matter effects.

## Contribution

It introduces a novel 5D R^2 gravity framework that derives a modified gravitational law, differing from General Relativity and providing an alternative explanation for galactic phenomena.

## Key findings

- Derivation of a 1/r gravitational law at large distances
- Proposal of a 5D cosmological model with singularity-free solutions
- Potential explanation for galactic rotation curves without dark matter

## Abstract

Galactic rotation curves and lack of direct observations of Dark Matter may indicate that General Relativity is not valid (on galactic scale) and should be replaced with another theory. There is the only variant of Absolute Parallelism which solutions are free of arising singularities, if D=5 (there is no room for changes). This variant does not have a Lagrangian, nor match GR: an equation of `plain' R^2-gravity (ie without R-term) is in sight instead. Arranging an expanding O_4-symmetrical solution as the basis of 5D cosmological model, and probing a universal_function of mass distribution (along very-very long the extra dimension) to place into bi-Laplace equation (R^2 gravity), one can derive the Law of Gravitation: 1/r^2 transforms to 1/r with distance (not with acceleration).