Exact modifications on a vacuum spacetime due to a gradient bumblebee field at its vacuum expectation value

Abstract

This work belongs to the context of the standard-model extension, in which a Lorentz symmetry violation is induced by a bumblebee field as it acquires a nonzero vacuum expectation value. The mathematical formulation of a generic bumblebee model and its associated dynamical equations are presented. Then, these equations are considered for the vacuum and a substantial simplification is performed for the particular case of a gradient bumblebee field at its vacuum expectation value. After some further manipulation, a method to easily find solutions to the model is developed, in which the exact effect on the spacetime description due to the presence of this bumblebee field is explicitly provided. As some examples, the method is applied to determine the implications of the bumblebee field on the Schwarzschild spacetime and also on a rotating one. A previously published solution is recovered and some new ones are obtained. In the rotating situation, a simple solution is found which contains both the Kerr solution and the already published one as special cases. It is also shown its distinguished surfaces are still given by the same corresponding expressions for the Kerr solution. In conclusion, the mathematical improvement made is considered to be a significant contribution to the theory as a powerful tool to investigate its many aspects and consequences.

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• Lorentz violation induces isospectrality breaking in Einstein-Bumblebee gravity theory
• Quasinormal Modes, Grebody Factors, and Hawking Radiation Sparsity of Black Holes Influenced by a Global Monopole Charge in Kalb-Ramond Gravity
• Testing black holes with cosmological constant in Einstein-bumblebee gravity through the black hole shadow using EHT data and deflection angle
• Braneworlds in bumblebee gravity
• Exact Taub-NUT-like Black Holes in Einstein-bumblebee gravity: their thermodynamics and thermodynamic topology
• Probing Lorentz-violating effects via precession and accretion disk images in a rotating bumblebee spacetime
• Cosmology in the presence of diffeomorphism-violating, nondynamical background fields