论暗物质在星系晕中的几何效应
On Dark Matter As A Geometric Effect in the Galactic Halo
摘要：
在球对称时空中，利用修正的引力理论导出的几何物态方程，考虑了旋转曲线平坦的条件，得到了星系晕中暗物质分布的一些特征。为了测量星系晕中暗物质的状态方程，我们提供了一个考虑到修改后的$f(X)$引力理论的一般形式。这里，$f(X)$是$X \in \{ R, \mathcal{G}, T \}$的一般函数，其中$R, \mathcal{G}$和$T$分别是Ricci标量、Gauss-Bonnet标量和扭转标量。这些理论得出，平坦的旋转曲线是修正引力理论所容纳的附加几何结构的结果。构造了一个几何状态方程$w_{_X} \equiv p_{_X} / ρ_{_X}$，并从普通物质状态方程的某些值出发，推导了星系星系晕中暗物质的一些性质。
英文摘要：
We obtain more straightforwardly some features of dark matter distribution in the halos of galaxies by considering the spherically symmetric space-time, which satisfies the flat rotational curve condition, and the geometric equation of state resulting from the modified gravity theory. In order to measure the equation of state for dark matter in the galactic halo, we provide a general formalism taking into account the modified $f(X)$ gravity theories. Here, $f(X)$ is a general function of $X \in \{ R, \mathcal{G}, T \}$, where $R, \mathcal{G}$ and $T$ are the Ricci scalar, the Gauss-Bonnet scalar and the torsion scalar, respectively. These theories yield that the flat rotation curves appear as a consequence of the additional geometric structure accommodated by those of modified gravity theories. Constructing a geometric equation of state $w_{_X} \equiv p_{_X} / ρ_{_X}$ and inspiring by some values of the equation of state for the ordinary matter, we infer some properties of dark matter in galactic halos of galaxies.
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