Bose–Einstein condensates near charged noncommutative inspired black holes

Abstract

In the present work, we investigate the Bose–Einstein condensates (BECs) on electrically charged noncommutative-inspired (NCi) black holes (BHs). The NC parameter represents a quantum correction that modifies spacetime geometry by introducing a minimal length scale. This impacts the BH’s effective gravitational field and, consequently, the dynamics of nearby scalar fields. The BEC is represented by a massive scalar field governed by the Klein–Gordon equation with a self-interaction term, assuming the scalar field is uncharged and devoid of self-gravitation and the mass parameter of the scalar field to be sufficiently small that may allow conditions to be a candidate for dark-matter clouds. We start our study by analyzing the properties of the event horizon and the mass profiles of NCi BH inside it. The BH charge and the NC parameters, , space are also studied. Then, we analyze the effective potential of a test scalar field in both radial and tortoise coordinates for the different values of the BH charge, the NC, and the scalar field mass parameters. Finally, we study the density function in the Thomas–Fermi approximation, in which the condensate is located in a spherical shell. The parameters Q and Θ can slightly modify the condensed density distribution.