Revisiting galactic rotation curves given a noncommutative-geometry background

TL;DR

This paper explores how noncommutative geometry, modeled with Lorentzian distribution instead of Gaussian, can explain galactic rotation curves without dark matter, and demonstrates the importance of smearing effects for stability.

Contribution

It introduces a simpler Lorentzian distribution to model noncommutative effects and proves that smearing is essential and sufficient for stability in galactic models.

Findings

Lorentzian distribution effectively models galactic rotation curves.

Smearing effect is necessary for stability.

Noncommutative geometry can explain rotation curves without dark matter.

Abstract

It was shown earlier by Rahaman et al. that a noncommutative-geometry background can account for galactic rotation curves without the need for dark matter. The smearing effect that characterizes noncommutative geometry is described by means of a Gaussian distribution intended to replace the Dirac delta function. The purpose of this paper is two-fold: (1) to account for the galactic rotation curves in a more transparent and intuitively more appealing way by replacing the Gaussian function by the simpler Lorentzian distribution proposed by Nozari and Mehdipour and (2) to show that the smearing effect is both a necessary and sufficient condition for meeting the stability criterion.