Quantum point particle approximation of spinning black holes and compact stars

TL;DR

This paper develops a quantum scattering amplitude approach to model the classical dynamics of spinning compact objects, providing a novel effective Hamiltonian valid at the first post-Minkowskian order for arbitrary spins, aiding gravitational wave physics.

Contribution

It introduces the first post-Minkowskian order Hamiltonian for spinning bodies valid to all orders in spin, advancing the theoretical modeling of binary systems in gravitational wave research.

Findings

First PM order Hamiltonian for arbitrary spinning bodies.

Extension challenges to second PM order discussed.

Framework based on quantum scattering amplitudes for classical physics.

Abstract

Gravitational wave observatories targeted for compact binary coalescence, such as LIGO and VIRGO, require various theoretical inputs for their efficient detection. One of such inputs are analytical description of binary dynamics at sufficiently separated orbital scales, commonly known as post-Newtonian dynamics. One approach for determining such two-body effective Hamiltonians is to use quantum scattering amplitudes. This dissertation aims at an improved understanding of classical physics of spinning bodies in quantum scattering amplitudes, for application to the problem of effective two-body Hamiltonians. The main focus will be on spin-induced higher-order multipole moments. In this dissertation results for the first post-Minkowskian order (linear in Newton's constant $G$ and to all orders in relative momentum $p^2$) Hamiltonian that is valid for arbitrary compact spinning bodies to all orders in spin is presented. Next, obstruction and prospects for the formulation's extension to second post-Minkowskian order is discussed, based on an equivalent loop order quantum field theory computations. This dissertation is based on the works [1-4].