Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction

TL;DR

This paper employs a Kaluza-Klein reduction within an effective field theory framework to compute the next-to-leading order gravitational spin-spin interaction between two spinning objects, simplifying calculations and confirming results with the ADM formalism.

Contribution

It demonstrates that KK reduction simplifies NLO spin-spin interaction calculations and establishes the equivalence between EFT and ADM Hamiltonian formalisms.

Findings

KK reduction simplifies NLO calculations.

Results agree with ADM Hamiltonian formalism.

Clarifies discrepancy with previous EFT results.

Abstract

We use the recently proposed Kaluza-Klein (KK) reduction over the time dimension, within an effective field theory (EFT) approach, to calculate the next to leading order (NLO) gravitational spin1-spin2 interaction between two spinning compact objects. It is shown here that to NLO in the spin1-spin2 interaction, the reduced KK action within the stationary approximation is sufficient to describe the gravitational interaction, and that it simplifies calculation substantially. We also find here that the gravito-magnetic vector field defined within the KK decomposition of the metric mostly dominates the mediation of the interaction. Our results coincide with those calculated in the ADM Hamiltonian formalism, and we provide another explanation for the discrepancy with the result previously derived within the EFT approach, thus demonstrating clearly the equivalence of the ADM Hamiltonian formalism and the EFT action approach.