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

Abstract

It is shown, that self-gravitating systems can be classified by a dimensionless constant positive number $\kappa = S T / E$, which can be determined from the (global) values for the entropy, temperature and (total) energy. The Kerr-Newman black hole family is characterized by $\kappa$ in the range $0-1/2$, depending on the dimensionless ratios of angular momentum and charge squared to the horizon area, $J/A$ and $Q^2/A$. By analyzing the most general case of an ultra-relativistic ideal gas with non-zero chemical potential it is shown, that $\kappa$ is an important parameter which determines the (local) thermodynamic properties of an ultra-relativistic gas. $\kappa$ only depends on the chemical potential per temperature $u = \mu / T$ and on the ratio of bosonic to fermionic degrees of freedom $r_F = f_B / f_F$. A gas with zero chemical potential has $\kappa = 4/3$. Whenever $\kappa < 4/3$ 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 $\kappa$ 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.