Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: a numerical approach

Abstract

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.