Calculation of radiation reaction effect on orbital parameters in Kerr spacetime
Calculation of radiation reaction effect on orbital parameters in Kerr spacetime
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DOI：
10.1093/ptep/ptv092
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发表时间：
2015-05
期刊：
影响因子：
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通讯作者：
N. Sago;R. Fujita
中科院分区：
文献类型：
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作者：
N. Sago;R. Fujita
我们计算了围绕克尔黑洞运行的点粒子在引力辐射作用下轨道参数的长期变化。为此，我们使用了一阶黑洞微扰理论中的后牛顿（PN）近似，并对轨道偏心率进行了扩展。在这项工作中，计算完成了四阶后牛顿（4PN）和六阶的偏心率，包括黑洞吸收引力波的影响。我们证实，在克尔的情况下，吸收的影响出现在粒子能量长期变化的2.5PN阶之上，并可能诱发超辐射，如先前已知的圆形轨道。此外，我们发现当轨道平面相对于中心黑洞的赤道平面倾斜时，超辐射可能会被抑制。我们还通过与数值结果的比较研究了4PN公式的准确性。如果我们要求4PN公式的相对误差小于$10^{-5}$，则满足该条件的参数区域在$e=0.1$时为$p\gtrsim 50$，在$e=0.4$时为$p\gtrsim 80$，在$e=0.7$时为$p\gtrsim 120$，几乎不考虑黑洞的倾角和自旋，其中$p$和$e$分别是半垂直轨道和轨道的偏心率。该区域可以进一步用指数恢复法扩展到$p\gtrsim 40$当$e=0.1$, $p\gtrsim 60$当$e=0.4$, $p\gtrsim 100$当$e=0.7$。虽然引力波的数据分析还需要更高阶的PN近似计算和轨道偏心率展开，但本文的结果相对于以往在2.5PN阶的工作是一个重要的改进，特别是对于大的$p$区域。
We calculate the secular changes of the orbital parameters of a point particle orbiting a Kerr black hole, due to the gravitational radiation reaction. For this purpose, we use the post-Newtonian (PN) approximation in the first order black hole perturbation theory, with the expansion with respect to the orbital eccentricity. In this work, the calculation is done up to the fourth post-Newtonian (4PN) order and to the sixth order of the eccentricity, including the effect of the absorption of gravitational waves by the black hole. We confirm that, in the Kerr case, the effect of the absorption appears at the 2.5PN order beyond the leading order in the secular change of the particle's energy and may induce a superradiance, as known previously for circular orbits. In addition, we find that the superradiance may be suppressed when the orbital plane inclines with respect to the equatorial plane of the central black hole. We also investigate the accuracy of the 4PN formulae by comparing to numerical results. If we require that the relative errors in the 4PN formulae are less than $10^{-5}$, the parameter region to satisfy the condition will be $p\gtrsim 50$ for $e=0.1$, $p\gtrsim 80$ for $e=0.4$, and $p\gtrsim 120$ for $e=0.7$ almost irrespective of the inclination angle nor the spin of the black hole, where $p$ and $e$ are the semi-latus rectum and the eccentricity of the orbit. The region can further be extended using an exponential resummation method to $p\gtrsim 40$ for $e=0.1$, $p\gtrsim 60$ for $e=0.4$, and $p\gtrsim 100$ for $e=0.7$. Although we still need the higher order calculations of the PN approximation and the expansion with respect to the orbital eccentricity to apply for data analysis of gravitational waves, the results in this paper would be an important improvement from the previous work at the 2.5PN order, especially for large $p$ region.