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arXiv 2112.08142gr-qc
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弱场极限下相对论性大质量粒子的Kerr-Newman黑洞透镜

Kerr-Newman black hole lensing of relativistic massive particles in the weak field limit

Guansheng He, Wenbin Lin

摘要:

在弱场极限下系统地研究了Kerr-Newman黑洞对相对论中性大质量粒子的引力透镜效应。基于Boyer-Lindquist坐标系下的Kerr-Newman度规,我们首先在第三种后闵可夫斯基近似下导出了大质量粒子赤道引力偏转角的解析形式。所得的弯曲角,这是一致的结果,在以前的工作中,被采用来解决流行的Virbhadra-Ellis透镜方程。因此,在标准微扰理论的框架内,在弱偏转极限之外,获得了粒子源的初级和次级图像的主要可观测性质的解析表达式。观测量包括各个图像的位置、放大率和重力时间延迟、微分时间延迟、总放大率和质心位置。由此得到了大质量粒子的初速度偏离光速对透镜像观测量的修正效应的显式形式。最后,作为形式主义的应用,银河系中心的超大质量黑洞,人马座A $^{\ast}$,被建模为一个克尔-纽曼透镜。速度引起的校正效应的实际透镜观测量的大小,以及在这种情况下检测到它们的可能性进行了分析。

英文摘要:

The gravitational lensing of relativistic neutral massive particles caused by a Kerr-Newman black hole is investigated systematically in the weak-field limit. Based on the Kerr-Newman metric in Boyer-Lindquist coordinates, we first derive the analytical form of the equatorial gravitational deflection angle of a massive particle in the third post-Minkowskian approximation. The resulting bending angle, which is found to be consistent with the result in the previous work, is adopted to solve the popular Virbhadra-Ellis lens equation. The analytical expressions for the main observable properties of the primary and secondary images of the particle source are thus obtained beyond the weak-deflection limit, within the framework of standard perturbation theory. The observables include the positions, magnifications, and gravitational time delays of the individual images, the differential time delay, and the total magnification and centroid position. The explicit forms of the correctional effects induced by the deviation of the initial velocity of the massive particle from the speed of light on the observables of the lensed images are then achieved. Finally, serving as an application of the formalism, the supermassive black hole at the Galactic center, Sagittarius A$^{\ast}$, is modeled to be a Kerr-Newman lens. The magnitudes of the velocity-induced correctional effects on the practical lensing observables as well as the possibilities to detect them in this scenario are also analyzed.

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