Gravitational-Bumblebee perturbations: Exact decoupling and isospectrality
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909012734246912 |
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| author | Liu, Hui-Fa Liu, Wentao Liu, Yu-Xiao Su, Qi Zeng, Ding-fang |
| author_facet | Liu, Hui-Fa Liu, Wentao Liu, Yu-Xiao Su, Qi Zeng, Ding-fang |
| contents | In this paper, we present the exact decoupling of the full metric and bumblebee field perturbations in a Schwarzschild-like background. The coupled system reduces to four decoupled master equations, revealing in each parity sector a Schwarzschild-like gravitational sector and a Lorentz-violating Maxwell-like vector sector. While Lorentz violation modifies the propagation speed of the emergent vector modes, we demonstrate that the gravitational master modes exhibit a ``dynamical immunity'' to the non-minimal Lorentz-violating coupling, and that the odd- and even-parity perturbations remain strictly isospectral. Our work provides a rare example in which Lorentz-violating couplings reshape the field reconstruction while leaving the gravitational ringdown spectrum intact. This mismatch in propagation speeds suggests a possible timing signature of bumblebee vector dynamics in black hole perturbations, offering a theoretical route to testing spontaneous Lorentz symmetry breaking in the era of multi-messenger astronomy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_02820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gravitational-Bumblebee perturbations: Exact decoupling and isospectrality Liu, Hui-Fa Liu, Wentao Liu, Yu-Xiao Su, Qi Zeng, Ding-fang General Relativity and Quantum Cosmology In this paper, we present the exact decoupling of the full metric and bumblebee field perturbations in a Schwarzschild-like background. The coupled system reduces to four decoupled master equations, revealing in each parity sector a Schwarzschild-like gravitational sector and a Lorentz-violating Maxwell-like vector sector. While Lorentz violation modifies the propagation speed of the emergent vector modes, we demonstrate that the gravitational master modes exhibit a ``dynamical immunity'' to the non-minimal Lorentz-violating coupling, and that the odd- and even-parity perturbations remain strictly isospectral. Our work provides a rare example in which Lorentz-violating couplings reshape the field reconstruction while leaving the gravitational ringdown spectrum intact. This mismatch in propagation speeds suggests a possible timing signature of bumblebee vector dynamics in black hole perturbations, offering a theoretical route to testing spontaneous Lorentz symmetry breaking in the era of multi-messenger astronomy. |
| title | Gravitational-Bumblebee perturbations: Exact decoupling and isospectrality |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.02820 |