Recent progress in spin calculations in the post-Newtonian framework and applications

TL;DR

This paper presents recent advances in deriving high-order post-Newtonian Hamiltonians for spinning binary systems and demonstrates their application to calculating the last stable circular orbit of black hole or neutron star binaries.

Contribution

It introduces the derivation of next-to-next-to-leading order spin-dependent Hamiltonians in the post-Newtonian framework and discusses their application to orbital stability analysis.

Findings

Derived high-order spin-orbit and spin(1)-spin(2) Hamiltonians

Validated the complex Hamiltonian results through consistency checks

Applied Hamiltonians to determine the last stable circular orbit

Abstract

Recently we derived the next-to-next-to-leading order post-Newtonian Hamiltonians at spin-orbit and spin(1)-spin(2) level for a binary system of compact objects. In this talk the derivation of them will be shortly outlined at an introductory level. We will also discuss some checks of our (complicated and long) results in the first part of the talk. In the second part we will show how to apply our results to the calculation of the last stable circular orbit of such a binary system of black holes or neutron stars.