论文标题
Mond的修改惯性公式的模型
Models of modified-inertia formulation of MOND
论文作者
论文摘要
描述了MOND的“修改惯性”公式的模型，并应用于非士兵多体系统。它们涉及运动的时间非局部方程。动量，角动量和能量是（非局部）定义的，其总值是为孤立系统保守的。这些模型可以做出所有显着的预测。然而，它们与某些二线预测中的现有“修改性奖励”公式不同。这些模型即使其成分的内部加速度很高，也正确描述了复合体在低速电场中的运动。它们表现出MOND外部田地效应（EFE），显示出与我们从修改的重大版本中所期望的一些重要差异：在一个模型的一个简单示例中，在主要的外部场上，确定EFE的内容为$μ（θ\ langle a__ {ex}} {ex}} \ rangle/a_0 a_0）$ s $ untim $ untim $ untim $ untum $μ（x）。曲线，与目前已知的修改性更严重公式的$μ（a_ {ex}/a_0）$相比。两个主要区别是，虽然$ a_ {ex} $是外部加速度的瞬时值，但$ \ langle a_ {ex} \ rangle $是它的一定时间平均值，而$θ> 1 $是额外的因素，取决于外部和内部场所变化的频率比。仅输入频率的比率，而$ A_0 $仍然是唯一的新尺寸常数。对于银河系中的圆形轨道上的系统（例如圆盘星系中的垂直动力学），第一个差异消失，因为$ \ langle a_ _ {ex} \ rangle = a__ {ex} $。但是，$θ$因子可以明显地增强Quench Mond效应的EFE，而不是在修饰的重力中推断出来的。还描述了一些精确的解决方案，例如旋转曲线，用于谐波力，以及一般的两体问题，在深处的政权中，这些问题将减少到单身问题。
Models of "modified-inertia" formulation of MOND are described and applied to nonrelativistic many-body systems. They involve time-nonlocal equations of motion. Momentum, angular momentum, and energy are (nonlocally) defined, whose total values are conserved for isolated systems. The models make all the salient MOND predictions. Yet, they differ from existing "modified-gravity" formulations in some second-tier predictions. The models describe correctly the motion of a composite body in a low-acceleration field even when the internal accelerations of its constituents are high. They exhibit a MOND external field effect (EFE) that shows some important differences from what we have come to expect from modified-gravity versions: In one, simple example of the models, what determines the EFE, in the case of a dominant external field, is $μ(θ\langle a_{ex}\rangle/a_0)$, where $μ(x)$ is the MOND `interpolating function' that describes rotation curves, compared with $μ(a_{ex}/a_0)$ for presently-known modified-gravity formulations. The two main differences are that while $a_{ex}$ is the momentary value of the external acceleration, $\langle a_{ex}\rangle$ is a certain time average of it, and that $θ>1$ is an extra factor that depends on the frequency ratio of the external- and internal-field variations. Only ratios of frequencies enter, and $a_0$ remains the only new dimensioned constant. For a system on a circular orbit in a galaxy (such as the vertical dynamics in a disc galaxy), the first difference disappears, since $\langle a_{ex}\rangle=a_{ex}$. But the $θ$ factor can appreciably enhance the EFE in quenching MOND effects, over what is deduced in modified gravity. Some exact solutions are also described, such as for rotation curves, for an harmonic force, and the general, two-body problem, which in the deep-MOND regime reduces to a single-body problem.
