Based on the framework of Kaniadakis’ statistics and its related kinetic theory, the Jeans instability for self-gravitational systems in the background of Eddington-inspired Born–Infield (EiBI) gravity is revisited. A dispersion relation generalizing the Jeans modes is derived by modifying the Maxwellian distribution to a family of power law distributions parameterized by the κ parameter. It is established that the κ -deformed Kaniadakis distribution has significant effects on the Jeans modes of the collisionless EiBI-gravitational systems. And as expected, in the limitation κ → 0, the corresponding results for Maxwellian case are recovered. The related result in the present work is valuable for the investigations involving the fields of astrophysics such as neutron stars, accretion disks, and relevant plasma physics, etc .

中文翻译：

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Eddington启发的Born-Infield重力中具有κ变形Kaniadakis分布的牛仔裤重力失稳

基于Kaniadakis的统计数据及其相关动力学理论的框架，在以爱丁顿为灵感的Born-Infield（EiBI）引力的背景下，重新考虑了自引力系统的Jeans不稳定性。通过将Maxwellian分布修改为由κ参数设置的幂定律分布族，可以得出使Jeans模式泛化的色散关系。可以确定，κ形变的Kaniadakis分布对无碰撞EiBI引力系统的Jeans模式具有重要影响。并如预期的那样，在限制κ→0中，恢复了麦克斯韦情况的相应结果。本工作的相关结果对于涉及中子星，吸积盘和相关等离子体物理等天体物理学领域的研究是有价值的。