标题： 分数引力中的 Jeans 分析 显示英文标题

标题： Jeans analysis in fractional gravity

摘要： 最近已被证明[A. Giusti, Phys. Rev. D 101, 124029 (2020)]，Milgrom的修改牛顿动力学(MOND)的特征可以从一个完全不同的框架中复制出来：牛顿力学的一个分数变体。为了进一步评估其有效性，需要在相关的天体物理情景中对该提议进行测试。在这里，我们研究其对Jeans引力不稳定性及相关现象的影响。我们考察了由引力约束的经典物质情景，并通过Schrödinger-Newton方法将我们的分析扩展到量子领域。我们还推导了一个与分数引力相关的广义Lane-Emden方程。通过将推导出的稳定性准则与观测到的Bok球状云的稳定性进行比较，我们建立了该理论参数的约束，以与观测数据一致。 显示英文摘要

摘要： It has recently been demonstrated [A. Giusti, Phys. Rev. D 101, 124029 (2020)] that characteristic traits of Milgrom's modified Newtonian dynamics (MOND) can be replicated from an entirely distinct framework: a fractional variant of Newtonian mechanics. To further assess its validity, this proposal needs to be tested in relevant astrophysical scenarios. Here, we investigate its implications on Jeans gravitational instability and related phenomena. We examine scenarios involving classical matter confined by gravity and extend our analysis to the quantum domain, through a Schr\"odinger-Newton approach. We also derive a generalized Lane-Emden equation associated with fractional gravity. Through comparisons between the derived stability criteria and the observed stability of Bok globules, we establish constraints on the theory's parameters to align with observational data.