The pulsational mode of gravitational collapse (PMGC) originating from the combined gravito-electrostatic interaction in complex dust molecular clouds (DMCs) is a canonical mechanism leading to the onset of astronomical structure formation dynamics. A generalized semi-analytic model is formulated to explore the effects of the Eddington-inspired Born-Infeld (EiBI) gravity, non-thermal (r,q)-distributed electrons, and dust-polarization force on the PMGC stability concurrently. The thermal ions are treated thermo-statistically with the Maxwellian distribution law and the non-thermal electrons with the (r,q)-distribution law. The constitutive partially ionized dust grains are modeled in the fluid fabric. A spherical normal mode analysis yields a generalized linear PMGC dispersion relation. Its oscillatory and propagation characteristics are investigated in a judicious numerical platform. It is found that an increase in the polarization force and positive EiBI parameter significantly enhances the instability, causing the DMC collapse and vice versa. The electron non-thermality spectral parameters play as vital stabilizing factors, and so on. Its reliability and applicability are finally outlined in light of astronomical predictions previously reported in the literature.

中文翻译：

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具有 （r，q） 分布电子的复杂 EiBI 引力极化天文云中的脉动模式稳定性


引力坍缩 （PMGC） 的脉动模式起源于复杂尘埃分子云 （DMC） 中重力-静电的联合相互作用，是导致天文结构形成动力学开始的典型机制。建立了一个广义半解析模型，以探索受 Eddington 启发的 Born-Infeld （EiBI） 引力、非热 （r，q） 分布电子和尘埃极化力同时对 PMGC 稳定性的影响。热离子用麦克斯韦分布定律进行热统计处理，用 （r，q） 分布定律对非热电子进行处理。在流体织物中对本构部分电离尘埃颗粒进行建模。球面正则模态分析可产生广义线性 PMGC 色散关系。在一个明智的数值平台中研究了它的振荡和传播特性。研究发现，极化力和正 EiBI 参数的增加显着增强了不稳定性，导致 DMC 崩溃，反之亦然。电子非热性光谱参数起着重要的稳定因子的作用，依此类推。它的可靠性和适用性最终根据文献中先前报道的天文预测进行了概述。