论文标题
通过移动的Kerr-Newman Black Hole的重力偏转光和巨大的粒子
Gravitational Deflection of Light and Massive Particle by a Moving Kerr-Newman Black Hole
论文作者
论文摘要
由于研究了一个径向移动的Kerr-Newman黑洞，包括光线的重力偏转，包括光线，任意恒定速度垂直于其角动量。在谐波坐标中，我们得出了测试粒子运动后的第二个运动后方程，并通过高准确性数值计算来解决它们。然后，我们专注于讨论由重力源到二阶偏转引起的运动校正。通过移动镜头获得光偏转角度至二阶的分析公式。对于以相对论速度移动的巨大粒子，Schwarzschild偏转角有两个不同的分析结果，直到先前的作品中报道的二阶，即$α（w）= 2 \ left（1+ \ frac {1} {w^2} \ right）\ frac {m} {m} {b}+3π\ left（\ frac {1} {4} {4}+\ frac {1} {1} {1} {w^2} {w^2} {w^2} \右） $α（w）= 2 \ left（1+ \ frac {1} {w^2} \ right）\ frac {m} {b}+\ left [3π\ left（\ frac {1} {1} {4} {4}+ \ frac {1} {w^2} \ right）+2 \ left（1- \ frac {1} {w^4} \ right）\ right] \ right] \ frac {m^2} {b^2}其中$ m，$ $ b，$和$ w $分别是镜头的质量，影响参数和粒子的初始速度。我们的数值结果与前者完全吻合。此外，在KERR几何形状中达到了大规模颗粒挠度的分析公式。最后，还分析了检测运动对二阶挠度的影响的可能性。
The gravitational deflection of test particles including light, due to a radially moving Kerr-Newman black hole with an arbitrary constant velocity being perpendicular to its angular momentum, is investigated. In harmonic coordinates, we derive the second post-Minkowskian equations of motion for test particles, and solve them by high-accuracy numerical calculations. We then concentrate on discussing the kinematical corrections caused by the motion of the gravitational source to the second-order deflection. The analytical formula of light deflection angle up to second order by the moving lens is obtained. For a massive particle moving with a relativistic velocity, there are two different analytical results for Schwarzschild deflection angle up to second order reported in the previous works, i.e., $α(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+3π\left(\frac{1}{4}+\frac{1}{w^2}\right)\frac{M^2}{b^2}$ and $α(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+\left[3π\left(\frac{1}{4}+\frac{1}{w^2}\right)+2\left(1-\frac{1}{w^4}\right)\right]\frac{M^2}{b^2}$, where $M,$ $b,$ and $w$ are the mass of the lens, impact parameter, and the particle's initial velocity, respectively. Our numerical result is in perfect agreement with the former. Furthermore, the analytical formula for massive particle deflection up to second order in the Kerr geometry is achieved. Finally, the possibilities of detecting the motion effects on the second-order deflection are also analyzed.
