Gravitational waves from spinning binary black holes at the leading post-Newtonian orders at all orders in spin

TL;DR

This paper derives analytical expressions for gravitational wave energy and modes from rapidly spinning black hole binaries, considering all orders of spin effects at leading post-Newtonian order, focusing on aligned spins in quasi-circular orbits.

Contribution

It provides the first all-orders-in-spin analytical formulas for binding energy and gravitational wave flux at leading post-Newtonian order for aligned-spin black hole binaries.

Findings

Analytical expressions for binding energy and flux are finite polynomials in spins.

Results are valid for quasi-circular orbits with aligned spins.

Expressions are simple and nonperturbative in spins.

Abstract

We determine the binding energy, the total gravitational wave energy flux, and the gravitational wave modes for a binary of rapidly spinning black holes, working in linearized gravity and at leading orders in the orbital velocity, but to all orders in the black holes' spins. Though the spins are treated nonperturbatively, surprisingly, the binding energy and the flux are given by simple analytical expressions which are finite (respectively third- and fifth-order) polynomials in the spins. Our final results are restricted to the important case of quasi-circular orbits with the black holes' spins aligned with the orbital angular momentum.