Post-Newtonian corrections to the motion of spinning bodies in NRGR

TL;DR

This paper extends the NRGR formalism to include spin and multipole effects, deriving Hamiltonians for spinning bodies and analyzing finite size effects, tidal deformations, and their contributions to motion.

Contribution

It introduces a comprehensive description of spinning extended bodies in NRGR, including spin-orbit, spin-spin, quadrupole-spin Hamiltonians, and finite size effects at leading order.

Findings

Tidal effects start at O(v^6) for general objects.

Self-induced effects can appear at leading order.

Results agree with known cases.

Abstract

In this paper we include spin and multipole moment effects in the formalism used to describe the motion of extended objects recently introduced in hep-th/0409156. A suitable description for spinning bodies is developed and spin-orbit, spin-spin and quadrupole-spin Hamiltonians are found at leading order. The existence of tidal, as well as self induced finite size effects is shown, and the contribution to the Hamiltonian is calculated in the latter. It is shown that tidal deformations start formally at O(v^6) and O(v^10) for maximally rotating general and compact objects respectively, whereas self induced effects can show up at leading order. Agreement is found for the cases where the results are known.