# Tully-Fisher-relation

Title: Is the Tully-Fisher relation the result of a quantum gravitational effect?

Language: GB/USA.

French matriculation: ISBN 978-2-36923-150-9, EAN 9782369231509.

version: 2.

Publication: 2 January 2023.

Number of pages: 18.

Comments: This is a deeply reworked version of the v1:

## Abstract

A. Einstein's theory of gravitation predicts that any spinning gravitational source drags the spacetime structure with it: it is the so-called Thirring-Lense effect. This effect has been measured (LAGEOS, Gravity Probe B, etc.) and confirmed in 2015.

This document goes a step further in proposing a simple hypothesis: Any Thirring-Lense effect generates a massive Klein-Gordon wave.

The Klein-Gordon equation is analyzed with algebraic tools relating it to the theory of deformed algebras. This approach associates a deformed angular momentum (dam) with each wave at each instant. The dam can be non-trivially decomposed. Two constraints can be imposed to the kern of the decomposition to incorporate it in a theory of quantum mechanics.

In this document, I consider any galaxy with a spinning center, and I apply that way of thinking in supposing that the Thirring-Lense effect induces a massive Klein-Gordon wave.

I recall the specificity of the Thirring-Lense effect, around the earth and in general, analyze the Klein-Gordon equation in a A.D.M.-like context with the eyes of the theory studying the deformed tensor products, discover the kerns and write the constraints that must be respected to build Hartree-like states. In a second step, I confront these constraints with the usual formulation of the Thirring-Lense effect in general relativity.

It turns out that the second constraint is in fact a relation connecting the rotational speed of a given star at distance r of the center of the galaxy. I explain why I think that this relation is in accordance with the Tully-Fisher relation.

The demonstration suggests that the kinetic behavior of arms in spiral galaxies is the macroscopic and amplified expression of a quantum gravitational phenomenon.

Since the Tully-Fisher relation also governs these galaxies, I risk the question: ``Is the Tully-Fisher relation the result of a quantum gravitational effect?''