Variational and Scaling Properties of Self-Interacting Fluids and Their Mass Quantizations

Abstract

Several equilibria of self-interacting fluids are formulated by variational functionals. In the self-gravitating fluid, this is done by the total mass and the total energy functionals, and then the dynamical stability of the equilibrium is derived from its linearized stability. Next, the quantized condensation is shown as a critical phenomenon, using the scaling invariance of these functionals. Similarity to the Smoluchowski-Poisson equation is discussed, and then the effect of thermal radiation is studied.