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

## TL;DR

This paper explores the properties of smooth, spherically symmetric mass distributions in black hole models, revealing generic behaviors, horizon structures, and regular solutions that unify various physical entities like black holes, stars, and dark matter halos.

## Contribution

It introduces new smooth distribution models and derives exact solutions for regular black holes and related objects, extending the understanding of horizon structures and regularity conditions.

## Key findings

- De Sitter behavior at the origin is generic.
- Number of horizons depends on distribution inflection points.
- Mass-to-radius ratio limits regular black hole formation.

## Abstract

We discuss the generic properties of a general, smoothly varying, spherically symmetric mass distribution $\mathcal{D}(r,\theta)$, with no cosmological term ($\theta$ 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 $\mathcal{D}(0,\theta)$, (b) the geometry may posses up to $2(k+1)$ horizons depending solely on the total mass $M$ if the cumulative distribution of $\mathcal{D}(r,\theta)$ 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 $\theta$. 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 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.