Distributional noncommutative and quantum-corrected black holes, stars, and dark matter halos

Mustapha Azreg-Aïnou

Published 2017-06-14Version 1

We discuss the generic properties of any general mass distribution $\mathcal{D}(r,\theta)$ depending on one parameter $\theta$ and endowed with spherical symmetry. We show (a) that the de Sitter behavior of spacetime at the origin is generic and depends only on $\mathcal{D}(0,\theta)$, (b) that, due to the character of the cumulative distribution of $\mathcal{D}(r,\theta)$, the geometry may posses up to two horizons depending solely on the value of the total mass $M$, and (c) that no scalar invariant nor a thermodynamic entity diverges. We define new two-parameter mathematical distributions mimicking Gaussian and step-like functions and reduce to the Dirac distribution in the limit of vanishing parameter $\theta$. We use these distributions to derive in closed forms asymptotically flat, spherically symmetric, solutions that describe and model a variety of physical and geometric entities ranging from noncommutative black holes, quantum-corrected black holes to stars and dark matter halos for various scaling values of $\theta$. We show that the linear mass density $\pi c^2/G$ is an upper limit for regular-black-hole formation.