Thermodynamics of fluid elements in the context of saturated isothermal turbulence in molecular clouds

The presented paper is an attempt to investigate the dynamical states of an hydrodynamical isothermal turbulent self-gravitating system using some powerful tools of the classical thermodynamics. Our main assumption, inspired by the work of Keto et al. (2020), is that turbulent kinetic energy can be substituted for the macro-temperature of chaotic motion of fluid elements. As a proper sample for our system we use a model of turbulent self-gravitating isothermal molecular cloud which is at final stages of its life-cycle, when the dynamics is nearly in steady state. Starting from this point, we write down the internal energy for a physically small cloud's volume, and then using the first principle of thermodynamics obtain in explicit form the entropy, free energy, and Gibbs potential for this volume. Setting fiducial boundary conditions for the latter system (small volume) we explore its stability as a grand canonical ensemble. Searching for extrema of the Gibbs potential we obtain conditions for its minimum, which corresponds to a stable dynamical state of hydrodynamical system. This result demonstrates the ability of our novel approach.Comment: 7 pages, published version URL https://astro.bas.bg/AIJ/issues/n38/SDonkov.pd

Born-Infeld black holes coupled to a massive scalar field

Born-Infeld black holes in the Scalar-Tensor Theories of Gravity, in the case of massless scalar field, have been recently obtained. The aim of the current paper is to study the effect from the inclusion of a potential for the scalar field in the theory, through a combination of analytical techniques and numerical methods. The black holes coupled to a massive scalar field have richer causal structure in comparison to the massless scalar field case. In the latter case, the black holes may have a second, inner horizon. The presence of potential for the scalar field allows the existence of extremal black holes for certain values of the mass of the scalar field and the magnetic (electric) charge of the black hole. The linear stability against spherically symmetric perturbations is studied. Arguments in favor of the general stability of the solutions coming from the application of the "turning point" method are also presented.Comment: 26 pages, 16 figure