Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: A numerical approach
Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: A numerical approach
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绕克尔黑洞运行的粒子的引力波通量达到后牛顿第 20 阶：数值方法
DOI：
10.1103/physrevd.90.044025
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发表时间：
2014
影响因子：
5
通讯作者：
Abhay Shah
中科院分区：
文献类型：
--
作者：
Abhay Shah
在这篇文章中，我们给出了关于克尔黑洞（质量$M$和自旋参数$a$）的圆形赤道轨道上的粒子在无限远处和视界处的能量通量（和角动量通量）的后牛顿（pN）系数，最高可达20 pN阶。当一个pN项不是$a/M$中的多项式并且包含无理数函数（如多函数）时，它被写成$a/M$的幂级数。这是通过数值计算通量来实现的，其精度大于$10^{600}$的1分之一。如此高的精度使我们能够提取pN系数的解析值，这些系数是超越数的线性组合，如欧拉常数，素数的对数和$\pi$的幂。我们还给出了在史瓦西黑洞圆周轨道上的粒子在视界处入射能量通量的22-pN膨胀（与自旋无关的pN膨胀）。
In this article we present the post-Newtonian (pN) coefficients of the energy flux (and angular momentum flux) at infinity and event horizon for a particle in circular, equatorial orbits about a Kerr black hole (of mass $M$ and spin-parameter $a$) up to 20-pN order. When a pN term is not a polynomial in $a/M$ and includes irrational functions (like polygamma functions), it is written as a power series of $a/M$. This is achieved by calculating the fluxes numerically with an accuracy greater than 1 part in $10^{600}$. Such high accuracy allows us to extract analytical values of pN coefficients that are linear combinations of transcendentals like the Euler constant, logarithms of prime numbers and powers of $\pi$. We also present the 22-pN expansion (spin-independent pN expansion) of the ingoing energy flux at the event horizon for a particle in circular orbit about a Schwarzschild black hole.