Static Spherical Vacuum Solution to Bumblebee Gravity with Time-like VEVs
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| Format: | Preprint |
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2025
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| _version_ | 1866917185135312896 |
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| author | Li, Hao Zhu, Jie |
| author_facet | Li, Hao Zhu, Jie |
| contents | The static spherical vacuum solution in a bumblebee gravity model where the bumblebee field \(B_μ\) has a one-component time-like vacuum expectation value \(b_μ\) is studied. We show that in general curved space-time solutions are not allowed and only the Minkowski space-time exists. However, it is surprising that non-trivial solutions can be obtained so long as a unique condition for the vacuum expectation \(b^2\equiv -b^μb_μ=2/κ\), where \(κ=8πG\), is satisfied. We argue that naturally these solutions are not stable since quantum corrections would invalidate the likely numerical coincidence, unless there are some unknown \emph{fine-tuning} mechanisms preventing any deviation from this condition. Nevertheless, the naked singularities and the photon sphere of these novel but peculiar solutions are discussed, and we show that the extremal Reissner-Nordstr{ö}m solution is a limit of one of our solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Static Spherical Vacuum Solution to Bumblebee Gravity with Time-like VEVs Li, Hao Zhu, Jie General Relativity and Quantum Cosmology The static spherical vacuum solution in a bumblebee gravity model where the bumblebee field \(B_μ\) has a one-component time-like vacuum expectation value \(b_μ\) is studied. We show that in general curved space-time solutions are not allowed and only the Minkowski space-time exists. However, it is surprising that non-trivial solutions can be obtained so long as a unique condition for the vacuum expectation \(b^2\equiv -b^μb_μ=2/κ\), where \(κ=8πG\), is satisfied. We argue that naturally these solutions are not stable since quantum corrections would invalidate the likely numerical coincidence, unless there are some unknown \emph{fine-tuning} mechanisms preventing any deviation from this condition. Nevertheless, the naked singularities and the photon sphere of these novel but peculiar solutions are discussed, and we show that the extremal Reissner-Nordstr{ö}m solution is a limit of one of our solutions. |
| title | Static Spherical Vacuum Solution to Bumblebee Gravity with Time-like VEVs |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.17957 |