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2022

Static spherical vacuum solutions in the bumblebee gravity model

Xu, Rui, Liang, Dicong, Shao, Lijing

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The bumblebee gravity model is a vector-tensor theory of gravitation where the vector field nonminimally couples to the Ricci tensor.

By investigating the vacuum field equations with spherical symmetry, we find two families of black-hole (BH) solutions in this model: one has a vanishing radial component of the vector field and the other has a vanishing radial component of the Ricci tensor.
When the coupling between the vector field and the Ricci tensor is set to zero, the first family becomes the Reissner-Nordstr\"om solution while the second family degenerates to the Schwarzschild solution with the vector field being zero.
General numerical solutions in both families are obtained for nonzero coupling between the vector field and the Ricci tensor.

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