Vector Superradiance without Separability: Instability Rates from the Worldline Effective Theory

@misc{cove2026vector,
  title = {{Vector Superradiance without Separability: Instability Rates from the Worldline Effective Theory}},
  author = {Keegan Cove and Jingping Li and Riccardo Penco},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20960},
  eprint = {2609.20960},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20960},
}

TY  - UNPB
TI  - Vector Superradiance without Separability: Instability Rates from the Worldline Effective Theory
AU  - Keegan Cove
AU  - Jingping Li
AU  - Riccardo Penco
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20960
UR  - https://arxiv.org/abs/2609.20960
AB  - We use a point-particle effective field theory to study the superradiant instability rates of an ultralight massive vector around a slowly rotating black hole. Earlier effective-theory treatments reported an apparent O(1) discrepancy with the rates obtained by solving the Proca equation on a fixed black-hole background, e.g. for the mode with j=1 and ℓ=2. We show that there is in fact no discrepancy: once the leading-order states in the degenerate {ℓ=0,ℓ=2} subspace are correctly identified, the effective theory (implemented here with the graviton integrated out exactly, and expanded in α only afterwards) reproduces \emph{all} of the j=1 Proca instability rates exactly, and it does so \emph{without} ever invoking the FKKS ansatz on which the full-theory calculation rests. Since it never relies on separability, the same approach applies, at least in principle, to rotating backgrounds and bodies that lack the hidden symmetries underlying that ansatz. The single ingredient beyond the far zone is a conservative worldline contact term, the static monopole response of the horizon in the parity-even j=1 Proca sector, which we fix by matching to the near zone. The same term shifts the fine-structure splitting of the bound states into exact agreement with the published Proca spectrum. In addition to providing a conceptually straightforward model of vector superradiance and resolving an apparent tension in the literature, we present this work to illustrate potential technical subtleties involving dissipative effects in point particle effective theories.
ER  -