On the origin of the matter-antimatter asymmetry in self-gravitating systems at ultra-high temperatures

It is shown, that self-gravitating systems can be classified by a dimensionless constant positive number κ = ST/E, which can be determined from the (global) values for the entropy, temperature and (total) energy. The Kerr-Newman black hole family is characterized by κ in the range 0−1/2, depending on the dimensionless ratios of angular momentum and charge squared to the horizon area, J/A and Q/A. By analyzing the most general case of an ultra-relativistic ideal gas with non-zero chemical potential it is shown, that κ is an important parameter which determines the (local) thermodynamic properties of an ultra-relativistic gas. κ only depends on the chemical potential per temperature u = μ/T and on the ratio of bosonic to fermionic degrees of freedom rF = fB/fF . A gas with zero chemical potential has κ = 4/3. Whenever κ < 4/3 the gas must acquire a non-zero chemical potential. This non-zero chemical potential induces a natural matter-antimatter asymmetry, whenever microscopic statistical thermodynamics can be applied. The recently discovered holographic solution describes a compact self gravitating black hole type object with an interior, well defined matter state. One can associate a local possibly observer-dependent value of κ to the interior matter, which lies in the range 2/3− 1 (for the uncharged case). This finding is used to construct an alternative scenario of baryogenesis in the context of the holographic solution, based on quasi-equilibrium thermodynamics.