Chandrasekhar's integral stability criterion for an equilibrium spherical cloud of a protostar, modified in the framework of non-Gaussian kappa-statistics

Within the framework of the non-extensive statistical mechanics of Kanyadakis, a generalization of the integral stability theorem of Chandrasekhar for the spherically symmetric distribution of matter and black radiation in an exoplanetary cloud in a state of gravitational equilibrium is obtained. For this purpose, the elements of deformed thermodynamics for an ideal gas, deformed canonical Gibbs distribution, as well as the effective gravitational constant, calculated in the formalisms of Kanyadakis and Verlinde, are used. In this, the deformation parameter $\kappa$ (kappa) measures the so-called degree of nonextensiveness of the cloud system. In addition, the modified thermodynamic properties of blackbody radiation, in particular, the analogue of Stefan's law for radiation energy and generalized expressions for the entropy, heat capacity and radiation pressure, are discussed in the context of $\kappa$-statistics. The presented method of combining the indicated anomalous physical processes provides an alternative to the classical procedure of Chandrasekhar's derivation of the well-known integral theorems for gas configurations in gravitational equilibrium, and restores all standard expressions in the limit $\kappa\to 0$.
The results obtained will be able, according to the author, to explain some astrophysical problems of stellar-planetary cosmogony, associated, in particular, with modeling the processes of joint formation and evolution of a protosun and an exoplanetary cloud from a single nebula.