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

Mustapha Azreg-Aïnou

doi:10.1140/epjc/s10052-018-5966-y

EPJ

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

Mustapha Azreg-Aïnou^*

Engineering Faculty, Başkent University, Bağlıca Campus, 06810, Ankara, Turkey

Received: 1 November 2017
Accepted: 2 June 2018
Published online: 9 June 2018

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 (1.) the de Sitter behavior of spacetime at the origin is generic and depends only on $\mathcal {D}(0,\theta )$ , (2.) the geometry may posses up to $$2(k+1)$$

horizons depending solely on the total mass M if the cumulative distribution of $\mathcal {D}(r,\theta )$ 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 $\theta$ . 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.

12 Internat. Congress of the Balkan Physical Union
July 8-12, 2025
Bucharest, Romania

EPJ

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

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