An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes
An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes
复制标题
克尔黑洞引起的光赤道弯曲角的渐近一致近似
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
J. Faber
中科院分区：
文献类型：
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作者：
N. Barlow;S. J. Weinstein;J. Faber
给出了任意自旋Kerr黑洞赤道轨道光折弯角随碰撞参数变化的精确闭合表达式。这个表达式是通过确保明确满足弱偏转和强偏转极限，同时通过渐近逼近的方法在碰撞参数的中间值保持精度来构造的(Barlow等人，2017年Q.J.Mech。APPL数学课。70 21-48)。为此，研究了极值黑洞前进轨道的强偏转极限，并确定了它的完全非零渐近行为。与黑洞模拟中使用的计算昂贵的椭圆积分相比，导出的近似式可能是一个有吸引力的替代方案。
An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al 2017 Q. J. Mech. Appl. Math. 70 21–48). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full non-vanishing asymptotic behavior is determined. The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations.