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arXiv 0912.0790gr-qcastro-ph.COhep-phhep-th
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双度量MOND重力

Bimetric MOND gravity

Mordehai Milgrom

备注：
18 pages. Published in Phys. Rev. D; minor changes to match published version
发表信息：
Phys.Rev.D80:123536,2009
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摘要：

本文提出了一种新的相对论性MOND公式，它包含两个独立的自由度：MOND度规g_mn和一个辅助度规g*_mn。主要思想取决于这样一个事实，即我们可以从两个度规的列维-奇维塔联系的差C^a_bc中形成张量，这些张量的作用就像引力加速度。在MOND的上下文中，我们可以从C^a_bc/a0的收缩中形成无量纲的“加速度”标量及其函数。我研究一类由引力拉格朗日密度b sqrt（g）R+a sqrt（g*）R* -2（gg*）^{1/4}f（k）a0^2M（U/a0^2）的作用量控制的双度量MOND理论，（g_mn，psi）+I*（g*_mn，chi），其中U是C^a_bc中的标量二次项，k=（g/g*）^{1/4}，并且允许存在与g*_mn单独耦合的孪生物质chi。特别地，我专注于标量U的一个有趣而简单的选择。这个理论只引入了一个新的常数a0;在a0趋于0的极限下，它简单地趋向于广义相对论，而在非相对论极限下，它趋向于一个唯象上有效的MOND理论。该理论很自然地给出了MOND和“暗能量“效应来自作用中的同一项，两者都由MOND常数a0控制。至于非相对论系统的引力透镜--相对论MOND理论的圣杯--该理论预测，控制超光速粒子运动的同一个势也以与GR相同的方式决定了透镜。最后一个结果可以用其他U的选择来修改，但透镜仍然是增强的，类似于MOND，具有有效的对数势。

英文摘要：

A new relativistic formulation of MOND is advanced, involving two metrics as independent degrees of freedom: the MOND metric g_mn, to which alone matter couples, and an auxiliary metric g*_mn. The main idea hinges on the fact that we can form tensors from the difference, C^a_bc, of the Levi-Civita connections of the two metrics, and these act like gravitational accelerations. In the context of MOND we can form dimensionless `acceleration' scalars, and functions thereof, from contractions of C^a_bc/a0. I look at a class of bimetric MOND theories governed by an action with the gravitational Lagrangian density b sqrt(g)R+a sqrt(g*) R* -2(gg*)^{1/4}f(k)a0^2M(U/a0^2), and with matter actions I(g_mn,psi)+I*(g*_mn,chi), with U a scalar quadratic in the C^a_bc, k=(g/g*)^{1/4}, and allowing for the existence of twin matter, chi, that couples to g*_mn alone. In particular, I concentrate on one interesting and simple choice of the scalar U. This theory introduces only one new constant, a0; it tends simply to General Relativity in the limit a0 goes to 0, and to a phenomenologically valid MOND theory in the nonrelativistic limit. The theory naturally gives MOND and "dark energy" effects from the same term in the action, both controlled by the MOND constant a0. As regards gravitational lensing by nonrelativistic systems--a holy grail for relativistic MOND theories--the theory predicts that the same potential that controls massive-particle motion also dictates lensing in the same way as in GR. This last result can be modified with other choices of U, but lensing is still enhanced and MOND-like, with an effective logarithmic potential.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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