The Planckonions

We consider a spherically symmetric stellar configuration with a density profile $ρ(r)=\frac{c^2}{8πG r^2}$. 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 $P(r)=-ρ(r)$. 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.

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