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

We discuss the generic properties of a general, smoothly varying, spherically symmetric mass distribution D(r,theta), with no cosmological term (. is a length scale parameter). Observing these constraints, we show that (1.) the de Sitter behavior of spacetime at the origin is generic and depends only on D(0,theta), (2.) the geometry may posses up to 2(k + 1) horizons depending solely on the total mass M if the cumulative distribution of D(r,theta) has 2k + 1 inflection points, and (3.) 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.. 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, quantumcorrected black holes to stars and dark matter halos for various scaling values of.. We show that the mass-to-radius ratio pi c(2)/G is an upper limit for regular-black-hole formation. Core-multi-shell and multi-shell regular black holes are also derived