Smoothed one-core and core--multi-shell regular black holes

Abstract

We discuss the generic properties of a general, smoothly varying, spherically symmetric mass distribution $\mathcal{D}(r,θ)$, with no cosmological term ($θ$ is a length scale parameter). Observing these constraints, we show that (a) the de Sitter behavior of spacetime at the origin is generic and depends only on $\mathcal{D}(0,θ)$, (b) the geometry may posses up to $2(k+1)$ horizons depending solely on the total mass $M$ if the cumulative distribution of $\mathcal{D}(r,θ)$ has $2k+1$ inflection points, and (c) 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 $θ$. 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 $θ$. We show that the mass-to-radius ratio $πc^2/G$ is an upper limit for regular-black-hole formation. Core--multi-shell and multi-shell regular black holes are also derived.