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Static spherical vacuum solutions in the bumblebee gravity model

Rui XuDicong LiangLijing Shao
Sep 2022
摘要
The bumblebee gravity model is a vector-tensor theory of gravitation wherethe vector field nonminimally couples to the Ricci tensor. By investigating thevacuum field equations with spherical symmetry, we find two families ofblack-hole (BH) solutions in this model: one has a vanishing radial componentof the vector field and the other has a vanishing radial component of the Riccitensor. When the coupling between the vector field and the Ricci tensor is setto zero, the first family becomes the Reissner-Nordstr\"om solution while thesecond family degenerates to the Schwarzschild solution with the vector fieldbeing zero. General numerical solutions in both families are obtained fornonzero coupling between the vector field and the Ricci tensor. Besides BHsolutions, we also reveal the existence of solutions that have a nonvanishing$tt$-component of the metric on the supposed event horizon where the$rr$-component of the metric diverges while the curvature scalars are finite.These solutions are not supported by existing observations but present certainproperties that are of academic interests. We conclude the study by putting theBH solutions into tests against the Solar-system observations and the images ofsupermassive BHs.
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