A generating technique constructs exact bumblebee gravity solutions from vacuum spacetimes by adding b_μ b_ν to the metric, yielding non-unique Kerr-Newman-Taub-NUT-(A)dS extensions limited by global field reality.
Basically, all the expressions for the bumblebee field and the metric are the same as for the case of Reissner–Nordstr¨ om spacetime (see Sec
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Exact Kerr-Newman-(A)dS and other spacetimes in bumblebee gravity: employing a simple generating technique
A generating technique constructs exact bumblebee gravity solutions from vacuum spacetimes by adding b_μ b_ν to the metric, yielding non-unique Kerr-Newman-Taub-NUT-(A)dS extensions limited by global field reality.