Bumblebee radiation from neutral matter around a black hole

Abstract

We investigate bumblebee radiation generated by neutral matter orbiting a black hole with a radial spacelike vector vacuum. Starting from a point particle coupled minimally to the metric, we derive the curvature induced vector current and the potential response required by its conservation. For a localized circular source with no independent radial boundary current, this response gives $δV'=ξρ/4$. The axial vector source instead follows the radial transport of angular momentum and vanishes for circular motion. A slightly eccentric orbit excites an axial dipole at the orbital frequency $Ω$ and a quadrupole contribution at $2Ω$, with outgoing amplitudes proportional to $ev^3$ and $ev^4$, respectively, where $v=\sqrt{M/a}$. We construct their retarded response and obtain the leading coefficients through weak field matching. Reconstruction of the observer's tidal tensor gives the dipole strain $h_{\hat r\hatϕ}^{V,10}=ξ^2b^2μev^3\sinθ\cos[Ω(t-R)]/(8πR)$. The corresponding partial luminosity is $P_{B,10}^{\infty}=ξ^2b^2μ^2e^2v^{12}/(48πM^2)$ at the leading order. Remarkably, the ordinary neutral matter produces an additional radial transverse tidal signal even when the homogeneous gravitational master operator remains in Schwarzschild form.