Massive Higher Spins and Black Hole Interactions

TL;DR

This work develops a BRST-invariant Lagrangian framework for reducible massive bosonic higher-spin fields and constructs off-shell cubic (and, in principle, quartic) interactions. By diagonalizing reducible multiplets into irreducible components and formulating BRST-invariant cubic vertices for two massive and one massless field, it derives minimal-coupling structures that reproduce Kerr black hole gravitational-wave couplings in the classical limit, using spinor-helicity methods to guide the on-shell selection. The key contributions include explicit free-field BRST Lagrangians, a diagonalization scheme for higher-spin multiplets, and closed-form BRST-invariant vertices V(s,s,2) and V(s,s,1) expressed via invariants $(\mathcal{K}^{(i)}, \mathcal{Q}, \mathcal{Z})$, establishing a systematic route to model BH interactions in a higher-spin EFT framework. This approach connects higher-spin gauge theory techniques with post-Minkowskian black hole physics and gravitational-wave phenomenology.

Abstract

We give a brief introduction into the gauge invariant formulation of irreducible massive bosonic higher spin fields. We discuss both free Lagrangians and the ones which include cubic interactions. We demonstrate an application of these Lagrangians to a description of the interactions between Kerr black holes in a Post Minkowskian approximation.