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arXiv 0709.0046gr-qcastro-ph
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f(R)引力中作为几何效应的暗物质

Dark matter as a geometric effect in f(R) gravity

Christian G. Boehmer, Tiberiu Harko, Francisco S. N. Lobo

摘要:

在f(R)修正引力理论中,我们考虑了在稳定圆轨道上运动的试验粒子的切向速度的行为。在银河系尺度上进行的大量观测表明,大质量试验粒子(氢云)的旋转速度在距离银河系中心很远的地方趋于恒定值。分析了常速区f(R)模型中真空引力场方程,导出了度规张量的封闭形式的一般形式。爱因斯坦-希尔伯特拉格朗日量的修正形式为R^{1+n},参数n用切向速度表示。因此,我们发现,解释星系周围的测试粒子的运动只需要非常轻微的偏离经典广义相对论,修改的引力可以解释星系动力学,而不需要引入暗物质。

英文摘要:

We consider the behavior of the tangential velocity of test particles moving in stable circular orbits in f(R) modified theories of gravity. A large number of observations at the galactic scale have shown that the rotational velocities of massive test particles (hydrogen clouds) tend towards constant values at large distances from the galactic center. We analyze the vacuum gravitational field equations in f(R) models in the constant velocity region, and the general form of the metric tensor is derived in a closed form. The resulting modification of the Einstein-Hilbert Lagrangian is of the form R^{1+n}, with the parameter n expressed in terms of the tangential velocity. Therefore we find that to explain the motion of test particles around galaxies requires only very mild deviations from classical general relativity, and that modified gravity can explain the galactic dynamics without the need of introducing dark matter.

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