Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# On the Three Laws of Rotationally Supported Galaxies: The Observed Flattening of Rotation Curves, the Baryonic Tully-Fischer Relation and the Mass Discrepancy-acceleration Relation

Version 1 : Received: 11 October 2020 / Approved: 12 October 2020 / Online: 12 October 2020 (15:33:36 CEST)

How to cite: Alcauza, J. On the Three Laws of Rotationally Supported Galaxies: The Observed Flattening of Rotation Curves, the Baryonic Tully-Fischer Relation and the Mass Discrepancy-acceleration Relation. Preprints 2020, 2020100252 (doi: 10.20944/preprints202010.0252.v1). Alcauza, J. On the Three Laws of Rotationally Supported Galaxies: The Observed Flattening of Rotation Curves, the Baryonic Tully-Fischer Relation and the Mass Discrepancy-acceleration Relation. Preprints 2020, 2020100252 (doi: 10.20944/preprints202010.0252.v1).

## Abstract

In this paper we will find that, according to holographic principle {\cite{Holografico}} and thus considering Universe as the ensemble of $\aleph$ information bits or minimum particles of mass $m_{g}$, the contribution to galactic rotation curves can be due the rest of the visible Universe through a non-local collective gravitational interaction of all particles within the Universe's horizon, as a consequence of which all particles are gravitationally entangled and form a unified statistical ensemble. Therefore, we can to describe this global effect in terms of standard local Newtonian gravity within galaxies for the explanation of flatness galactic rotation curves as a possible alternative to the dark matter or MOND hypothesis. We will find a solution for the baryonic Tully-Fischer relation: $M_{b} = A v_{f}^4 \iff A = \left[a_{0}G \right]^{-1}$ with $a_{0} = \frac{cH_{0}}{2\pi}$, where $H_{0}$ is the Hubble constant at present Time $t_{0}$ and $M_{b}$, $G$ and $c$ are the galaxy baryonic mass, gravitational constant and constant speed of light in vacuum respectively. Also we will find the mass discrepancy-acceleration relation, thus obtaining a possible solution for each of the three laws of rotationally supported galaxies proposed in ({\cite{McGaugh}},{\cite{McGaugh1}}).

## Subject Areas

holographic principle; dark matter; MOND; flatness rotation curves; baryonic Tully- Fischer relation; mass discrepancy-acceleration relation

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