https://doi.org/10.1140/epjc/s10052-026-15814-w
Regular Article - Theoretical Physics
Gravitational waves in metric–affine bumblebee gravity
1
Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, Paraíba, Brazil
2
Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58429-900, Campina Grande, Paraíba, Brazil
3
Center for Theoretical Physics, Khazar University, 41 Mehseti Street, 1096, Baku, Azerbaijan
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
21
March
2026
Accepted:
7
May
2026
Published online:
26
May
2026
Abstract
We study the propagation and emission of gravitational waves in the metric–affine formulation of the bumblebee model, where spontaneous Lorentz symmetry breaking arises from a vector field acquiring a nonvanishing vacuum expectation value. Working in the geometric–optics limit of the linearized theory, we derive the modified dispersion relation governing the graviton modes and show that it depends on the orientation of the wave vector relative to the background vector. The polarization sector is examined for timelike and spacelike configurations of the Lorentz-violating vacuum. In both cases only two independent tensor modes propagate, although their propagation properties and tensor structure depend on the orientation of the background field. We then construct the retarded Green function associated with the modified wave operator and determine the radiation-zone produced by localized sources. In the timelike configuration the Lorentz-violating effects appear through a modified propagation speed and an overall amplitude renormalization, leading to a shifted retarded time while preserving the quadrupole structure of the waveform. In contrast, the spacelike sector introduces anisotropic corrections to the quadrupole amplitude together with an additional contribution proportional to the third time derivative of the quadrupole moment. As an astrophysical application, the gravitational radiation emitted by a circular binary black-hole system is evaluated, allowing observational constraints on the Lorentz-violating combination 
to be estimated using multimessenger bounds from GW170817/GRB 170817A and waveform consistency requirements from gravitational wave observations.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
