太阳系中暗物质对光传播的影响
Influence of Dark Matter on Light Propagation in Solar System
摘要：
我们研究了太阳系中暗物质对光传播的影响。我们假定时空是球对称的，导出了爱因斯坦方程的近似解，该方程由中心天体（太阳）和围绕它的暗物质引起的引力作用组成，并将太阳系中的暗物质密度表示为简单的幂律形式：$\varrho(t, r) = ρ(t)(\ell/r)^k$，其中$t$是坐标时间; $r$，中心体的半径; $\ell$，归一化因子; $k$，表征暗物质密度与$r$相关性的指数;以及$ρ(t)$，时间的任意函数$t$。在此基础上，我们着重讨论了光的传播，得到了由暗物质引起的引力时滞和相对频移的附加修正。作为我们结果的应用，我们考虑了Krasinsky和Brumberg（2004）报道的天文单位的长期增长，发现很难为观测到的$d{\rm AU}/dt = 15 \pm 4 ~[{\rm m/century}]$提供解释。
英文摘要：
We investigated the influence of dark matter on light propagation in the solar system. We assumed the spherical symmetry of spacetime and derived the approximate solution of the Einstein equation, which consists of the gravitational attractions caused by the central celestial body, i.e. the Sun, and the dark matter surrounding it. We expressed the dark matter density in the solar system in the following simple power-law form, $\varrho(t, r) = ρ(t)(\ell/r)^k$, where $t$ is the coordinate time; $r$, the radius from the central body; $\ell$, the normalizing factor; $k$, the exponent characterizing $r$-dependence of dark matter density; and $ρ(t)$, the arbitrary function of time $t$. On the basis of the derived approximate solution, we focused on light propagation and obtained the additional corrections of the gravitational time delay and the relative frequency shift caused by the dark matter. As an application of our results, we considered the secular increase in the astronomical unit reported by Krasinsky and Brumberg (2004) and found that it was difficult to provide an explanation for the observed $d{\rm AU}/dt = 15 \pm 4 ~[{\rm m/century}]$.
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