The Planckonions

TL;DR

This paper introduces 'Planckonions', a spherically symmetric stellar model with a layered structure at Planck scales, satisfying Einstein's equations with negative pressure, mimicking black holes while avoiding singularities.

Contribution

It proposes a novel stellar configuration called 'Planckonions' with layered Planck-scale shells, satisfying TOV equations with negative pressure, and avoiding singularities unlike traditional black holes.

Findings

Satisfies TOV equations with negative pressure P(r)=-ρ(r)

Features layered structure with Planck-scale shells

Avoids central singularity by violating null energy conditions

Abstract

We consider a spherically symmetric stellar configuration with a density profile $\rho(r)=\frac{c^2}{8\pi G r^2} $. This configuration satisfies the Schwarzchild black hole condition $\frac {2GM}{c^2 R}=~1$ for every $ r =R $. We refer it as "Planckonion". The interesting thing about the Plankonion is that it has an onion like structure. The central sphere with radius of the Plank-lenght $ L_p=\sqrt{(\frac {2\hbar G}{c^3})}$ has one unit of the Planck-mass $M_p=\sqrt {(\frac {c\hbar}{2G})}$. Subsequent spherical shells of radial width $L_p$ contain exactly one unit of $M_p$. We study this stellar configuration using Tolman-Oppenheimer-Volkoff equation and show that the equation is satisfied if pressure $P(r)=-\rho(r)$. On the geometrical side, the space component of the metric blows up at every point. The time component of the metric is zero inside the star but only in the sense of a distribution (generalized function). The Planckonions mimic some features of black holes but avoid appearance of central singularity because of the violation of null energy conditions.