Ultralight dark matter halo structures around a noncommutative Euler-Heisenberg black hole spacetime

Abstract

Cosmological simulations of ultra-massive black-hole configurations in the early universe challenge the idealized assumption of vacuum black-hole solutions. In this respect, we propose noncommutative-smeared Euler-Heisenberg-type black hole solutions embedded in ultralight dark matter (fuzzy dark matter) configurations. We incorporate the effects of nonlinear Euler-Heisenberg electrodynamics and spacetime noncommutativity into the black hole metric, and analyze the influence of fuzzy dark matter on the dynamics of black hole geometry. To capture the distribution of ultralight dark matter halos, we employ the Einasto model, which provides a highly faithful morphology of halo configurations over an extensive mass range. We examine how noncommutativity, black-hole charge, and Euler-Heisenberg coupling affect the geometry of spacetime and halo features. The coupling of the equation of state σ = − P r with the Einasto profile gives rise to different smearing fuzzy black-hole structures for several parameter choices of shape, charge, and nonlinear correction. We analyze the horizon structure and the corresponding geodesic motion of test particles associated with the smeared fuzzy black-hole metric using the Euler-Heisenberg formalism. Furthermore, the stability of the proposed black hole geometry is examined by constructing scalar as well as electromagnetic field perturbations. We find that the ultralight halo configurations significantly alter the gravitational landscape of the black hole geometry, in combination with the effects arising from the point-like noncommutative and nonlinear electrodynamics interactions.