The “Planckonions”

Abstract

We consider a spherically symmetric stellar configuration with a density profile [Formula: see text]. This configuration satisfies the Schwarzchild black hole condition [Formula: see text] for every [Formula: see text]. We refer to it as “Planckonion”. The interesting thing about the Planckonion is that it has an onion-like structure. The central sphere with radius of the Planck-length [Formula: see text] has one unit of the Planck-mass [Formula: see text]. Subsequent spherical shells of radial width [Formula: see text] contain exactly one unit of [Formula: see text]. We study this stellar configuration using Tolman–Oppenheimer–Volkoff equation and show that the equation is satisfied if pressure [Formula: see text]. 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.