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arXiv 2209.04055gr-qcastro-ph.GA
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柯顿引力和84个星系自转曲线

Cotton gravity and 84 galaxy rotation curves

Junpei Harada

备注：
22 pages, 7 figures, 1 table, accepted for publication in Phys. Rev. D, v2: published version
发表信息：
Phys. Rev. D 106, 064044, 2022
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摘要：

最近，作为广义相对论的推广，人们提出了一种引力理论，其中引力场方程由Cotton张量描述。该理论允许对一个质点的引力势的额外贡献，该点质量随半径线性上升为$Φ= -GM/r + γr/2$，其中$G$是牛顿常数。系数$M$和$γ$是积分常数，应针对每个物理系统单独确定。当应用于星系时，应该为每个星系确定具有加速度维度的系数$γ$。这与必须确定每个星系的质量$M$是一样的。如果$γ$足够小，则线性势项在短距离处可以忽略不计，但在长距离处可以变得显著。事实上，它可能有助于河外星系。本文导出了适用于河外星系的Cotton引力的有效场方程。然后，我们使用有效场方程数值计算的84个旋转星系的样本的引力势。这84个星系的范围很广，从以恒星盘为主的螺旋星系到以气体为主的矮星系。我们不假设恒星盘、球或气体的径向密度分布;我们只使用观测数据。我们发现84个星系的自转曲线可以用观测到的重子分布来解释。这是由于棉花引力的灵活性，允许每个星系的积分常数$γ$。在柯顿引力的背景下，“暗物质“在某种意义上被自动包含为时空的曲率。因此，即使是被认为是由暗物质主导的星系也不需要暗物质。

英文摘要：

Recently, as a generalization of general relativity, a gravity theory has been proposed in which gravitational field equations are described by the Cotton tensor. That theory allows an additional contribution to the gravitational potential of a point mass that rises linearly with radius as $Φ= -GM/r + γr/2$, where $G$ is the Newton constant. The coefficients $M$ and $γ$ are the constants of integration and should be determined individually for each physical system. When applied to galaxies, the coefficient $γ$, which has the dimension of acceleration, should be determined for each galaxy. This is the same as having to determine the mass $M$ for each galaxy. If $γ$ is small enough, the linear potential term is negligible at short distances, but can become significant at large distances. In fact, it may contribute to the extragalactic systems. In this paper, we derive the effective field equation for Cotton gravity applicable to extragalactic systems. We then use the effective field equation to numerically compute the gravitational potential of a sample of 84 rotating galaxies. The 84 galaxies span a wide range, from stellar disk-dominated spirals to gas-dominated dwarf galaxies. We do not assume the radial density profile of the stellar disk, bulge, or gas; we use only the observed data. We find that the rotation curves of 84 galaxies can be explained by the observed distribution of baryons. This is due to the flexibility of Cotton gravity to allow the integration constant $γ$ for each galaxy. In the context of Cotton gravity, "dark matter" is in some sense automatically included as a curvature of spacetime. Consequently, even galaxies that have been assumed to be dominated by dark matter do not need dark matter.

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