Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates

TL;DR

This paper derives higher-order-in-spin interaction Hamiltonians for binary black holes by transforming the Kerr metric into approximate ADM coordinates and calculating source terms, advancing the modeling of black hole interactions.

Contribution

It introduces a method to obtain higher-order-in-spin Hamiltonians from Kerr geometry in approximate ADM coordinates, including source term calculations.

Findings

Derived higher-order-in-spin Hamiltonians for black-hole binaries.

Transformed Kerr metric into ADM coordinates up to order 1/r^4 and a^2.

Calculated distributional source terms for approximate solutions.

Abstract

The Kerr metric outside the ergosphere is transformed into ADM coordinates up to the orders $1/r^4$ and $a^2$, respectively in radial coordinate $r$ and reduced angular momentum variable $a$, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black-hole binaries are derived.