论文标题
弱挠度角的扰动方法
The perturbative approach for the weak deflection angle
论文作者
论文摘要
NULL和及时射线都经历了重力场中的轨迹弯曲。在这项工作中，我们系统地开发了一种扰动方法，以在任意静态和球形对称的空间以及任意静态和轴对称性镜的赤道平面中计算一般速度$ v $的射线偏转角。我们表明，最接近最接近的方法的扩展$ x_0 $限制仅取决于公制函数的渐近行为，而生成的集成始终是可集成的，从而以$ x_0 $ x_0 $或$ b $的串联形式产生偏转角度。使用此方法，在Schwarzschild，Reissner-Nordström和Kerr-Newman SpaceTimes分别为17-3，15-15和6-1的订单中，偏转角度作为$ x_0 $和$ b $的系列，用于具有一般速度的Lightrays和17-3，15-15和6订单。简要分析了冲击参数，速度和其他参数的影响。此外，我们表明，对于仅渐近函数的空间，也可以计算弱场极限中的挠度角。此外，结果表明，静态和对称的时空和静态和轴对称时空的偏转角仅取决于粒子的影响参数，粒子的速度，以及空间的有效ADM质量，而不是其他参数，但不取决于其他参数，而不是其他参数（例如电荷或角度或角度）。这些挠度角用于精确的重力镜头方程，并且源图像的相应表观角度也可以扰动地求解。
Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity $v$ in arbitrary static and spherically symmetric spacetimes and in equatorial plane of arbitrary static and axisymmetric spacetimes. We show that the expansion in the large closest approach $x_0$ limit depends on the asymptotic behavior of the metric functions only, and the generated integrand is always integrable, resulting in a deflection angle in a series form of either $x_0$ or $b$, the impact parameter. Using this method, the deflection angles as series of both $x_0$ and $b$ are found in Schwarzschild, Reissner-Nordström and Kerr-Newman spacetimes to 17-th, 15-th and 6-th orders respectively, for both lightrays and particles with general velocity. The effects of the impact parameter, velocity and other parameters of the spacatimes are briefly analyzed. Moreover, we show that for spacetimes whose metric functions are only asymptotically known, the deflection angle in the weak field limit can also be calculated. Furthermore, it is shown that the deflection angle in general static and spherically symmetric spacetime and equatorial plane of static and axisymmetric spacetime to the lowest non-trivial order, depends only on the impact parameter, velocity of the particle, and the effective ADM mass of the spacetime but not on other parameters such as charge or angular momentum. These deflection angles are used in an exact gravitational lensing equation and the corresponding apparent angles of the images of the source are also solved perturbatively.
