Comparing different realizations of modified Newtonian dynamics: Virial theorem and elliptical shells
Comparing different realizations of modified Newtonian dynamics: Virial theorem and elliptical shells
复制标题
比较修正牛顿动力学的不同实现：维里定理和椭圆壳
DOI：
10.1103/physrevd.81.087304
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发表时间：
2010
影响因子：
5
通讯作者：
B. Famaey
中科院分区：
文献类型：
--
作者：
HongSheng Zhao;B. Famaey
有几个修正的引力理论，旨在重现米尔格罗姆的经验公式，修正的牛顿动力学（MOND）。在这里，我们得到的静态弱场极限的上下文中的分析结果，其中两个（双度量MOND，导致一组给定的参数的准线性MOND，和贝肯斯坦的张量矢量标量）。在这个极限下，这些理论被构造为给出相同的球对称力场，但是它们的预言通常会有所不同。然而，对于这些理论的某些实现（其特征在于对它们的自由函数的特定选择），与牛顿对应物相比，系统的结合势能会增加一个常数，而与系统的形状和大小无关。在这种情况下，维里定理在这两个理论中是完全相同的，对于整个引力体系，甚至在球对称之外，尽管精确的力场是不同的。我们明确表明这两个理论产生的力场内的椭圆壳。然而，对于更一般的自由函数，维里定理在这两个理论中并不相同。最后，我们探讨了这些分析结果的后果的两体力。
There exists several modified gravity theories designed to reproduce the empirical Milgrom's formula, modified Newtonian dynamics (MOND). Here we derive analytical results in the context of the static weak-field limit of two of them (bimetric MOND, leading for a given set of parameters to the quasilinear MOND, and Bekenstein's Tensor-Vector-Scalar). In this limit, these theories are constructed to give the same force field for spherical symmetry, but their predictions generally differ out of it. However, for certain realizations of these theories (characterized by specific choices for their free functions), the binding potential-energy of a system is increased, compared to its Newtonian counterpart, by a constant amount independent of the shape and size of the system. In that case, the virial theorem is exactly the same in these two theories, for the whole gravity regime and even outside of spherical symmetry, although the exact force fields are different. We explicitly show this for the force field generated by the two theories inside an elliptical shell. For more general free functions, the virial theorems are, however, not identical in these two theories. We finally explore the consequences of these analytical results for the two-body force.