Dynamic Aspects of Bumblebee Gravity: Post-Newtonian Approach
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914575541075968 |
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| author | Zhu, Jie Li, Hao |
| author_facet | Zhu, Jie Li, Hao |
| contents | In this work, we investigate the dynamic aspects of Bumblebee gravity via the parameterized post-Newtonian method. We find that the PPN framework is self-consistent up to 1.5PN order if and only if $λ= -ξ/2$, which corresponds to a direct coupling between the Bumblebee field $B_μ$ and the Einstein tensor. The requirement of tachyonic stability restricts the Bumblebee potential to satisfy $V''(0)=0$. In the specific case where $λ= -ξ/2$, the resulting PPN metric yields non-vanishing values for the parameters $α_1$ and $α_2$, as well as a novel PPN potential $U_B$ that exhibits a logarithmic asymptotic growth. The vanishing of the potential $U_B$ necessitates the additional constraints $ξ= κ/2$ or $V^{(3)}(0) = 0$. These results signify the presence of preferred-frame effects, a direct consequence of the Lorentz symmetry breaking in the model. In the limit of small $\ell$, we obtain $α_2 \simeq -\ell_2$, which yields a constraint of $|\ell| \lesssim 1.6\times 10^{-9}$ based on pulsar timing observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17516 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamic Aspects of Bumblebee Gravity: Post-Newtonian Approach Zhu, Jie Li, Hao General Relativity and Quantum Cosmology High Energy Physics - Phenomenology In this work, we investigate the dynamic aspects of Bumblebee gravity via the parameterized post-Newtonian method. We find that the PPN framework is self-consistent up to 1.5PN order if and only if $λ= -ξ/2$, which corresponds to a direct coupling between the Bumblebee field $B_μ$ and the Einstein tensor. The requirement of tachyonic stability restricts the Bumblebee potential to satisfy $V''(0)=0$. In the specific case where $λ= -ξ/2$, the resulting PPN metric yields non-vanishing values for the parameters $α_1$ and $α_2$, as well as a novel PPN potential $U_B$ that exhibits a logarithmic asymptotic growth. The vanishing of the potential $U_B$ necessitates the additional constraints $ξ= κ/2$ or $V^{(3)}(0) = 0$. These results signify the presence of preferred-frame effects, a direct consequence of the Lorentz symmetry breaking in the model. In the limit of small $\ell$, we obtain $α_2 \simeq -\ell_2$, which yields a constraint of $|\ell| \lesssim 1.6\times 10^{-9}$ based on pulsar timing observations. |
| title | Dynamic Aspects of Bumblebee Gravity: Post-Newtonian Approach |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2605.17516 |