论文标题
肮脏的黑洞的弱挠度角
Weak deflection angle of a dirty black hole
论文作者
论文摘要
在本文中，我们介绍了schwarzschild黑洞的弱挠度角度，该黑洞被质量$ m $和厚度$Δr_{s} $包围的质量$ m $。 Gauss-bonnet定理是为渐近空间制定的，被发现在非常大的$δr_{s} $的第三阶中遭受了行为不良。使用有限距离的源和接收器的径向位置，我们使用Ishihara（\ textit {et al。}）方法得出了弱偏转角度的表达式至$ 1/Δr_{s} $的第三阶。结果表明，所需的暗物质厚度为$ \ sim2 \ sqrt {3mm} $，对于弱偏转角度的偏差。与阴影半径（$ \ sim \ sqrt {3mm} $）相比，这种厚度要求较高2。这意味着在检测一个人星系中检测暗物质效应的弱偏转角的使用要比使用阴影半径中的任何偏差要好。
In this paper, we present the weak deflection angle in a Schwarzschild black hole of mass $m$ surrounded by the dark matter of mass $M$ and thickness $Δr_{s}$. The Gauss-Bonnet theorem, formulated for asymptotic spacetimes, is found to be ill-behaved in the third-order of $1/Δr_{s}$ for very large $Δr_{s}$. Using the finite-distance for the radial locations of the source and the receiver, we derived the expression for the weak deflection angle up to the third-order of $1/Δr_{s}$ using Ishihara (\textit{et al.}) method. The result showed that the required dark matter thickness is $\sim2\sqrt{3mM}$ for the deviations in the weak deflection angle to occur. Such thickness requirement is better by a factor of 2 as compared to the deviations in the shadow radius ($\sim\sqrt{3mM}$). It implies that the use of the weak deflection angle in detecting dark matter effects in one's galaxy is better than using any deviations in the shadow radius.
