论文标题
Kiselev Black Hole Spacetime在弱场极限中的零和时型信号的挠度和重力镜头
Deflection and Gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit
论文作者
论文摘要
在这项工作中，我们研究了弱场限制中基斯列夫时空中无效信号的挠度和重力镜头，以研究状态参数$ω$方程的影响和物质量参数$ $α$。在此过程中，我们扩展了一种先前针对渐近平坦的空间开发的扰动方法，其度量函数具有整数功率渐近膨胀到可能是或可能不是渐近平坦但具有非整合功率扩展的情况。 It is found that in the asymptotically flat case ($-1/3<ω<0$) the deflection angles are expressable as quasi-power series of the dimensionless quantities $M/b,~b/r_{s,d}$ and $α/M^{1+3ω}$ where $M,~b,~r_{s,d}$ are respectively the lens mass, impact parameter and source/detector 半径。对于（$ -1 <ω<-1/3 $）的非质量平面外壳也存在类似的系列，但最接近的半径$ r_0 $替换$ b $。在渐近平坦（或非平板）情况下，$α$或减少$ω$的增加将增加（或增加）偏转角。由于所获得的挠度角度自然考虑了源和检测器的有限距离效应，因此我们可以建立一个精确的重力透镜方程，从中，图像的明显角度及其大型求解。发现通常对于渐近平面的情况，增加$α$或减少$ω$会增加图像的明显角度。尽管对于非质子平面外壳，但增加$α$或$ω$都会导致较小的表观角度。
In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter $ω$ and the matter amount parameter $α$. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case ($-1/3<ω<0$) the deflection angles are expressable as quasi-power series of the dimensionless quantities $M/b,~b/r_{s,d}$ and $α/M^{1+3ω}$ where $M,~b,~r_{s,d}$ are respectively the lens mass, impact parameter and source/detector radius. A similar series exists for the non-asymptotically flat case of ($-1<ω<-1/3$), but with the closest radius $r_0$ replacing $b$. In the asymptotically flat (or non-flat) case, the increase of $α$ or decrease of $ω$ will increase (or increase) the deflection angle. Since the obtained deflection angles naturally take into account the finite distance effect of the source and the detector, we can establish an exact gravitational lensing equation, from which the apparent angles of the images and their magnifications are solved. It is found that generally for the asymptotically flat case, increasing $α$ or decreasing $ω$ will increase the apparent angles of the images. While for the non-asymptotically flat case, increasing $α$ or $ω$ will both lead to smaller apparent angles.
