Jeans Gravitational Instability with $\kappa$-Deformed Kaniadakis Distribution

The Jeans instabilities in an unmagnetized, collisionless, isotropic self-gravitating matter system are investigated in the context of $\kappa$-deformed Kaniadakis distribution based on kinetic theory. The result shows that both the growth rates and critical wave numbers of Jeans instability are lower in the $\kappa$-deformed Kaniadakis distributed self-gravitating matter systems than the Maxwellian case. The standard Jeans instability for a Maxwellian case is recovered under the limitation $\kappa =0$. (paper)