An exact Simpson-Visser family in bumblebee gravity

Abstract: We construct an exact Simpson-Visser solution in metric bumblebee gravity, supported by a phantom scalar, magnetic nonlinear electrodynamics, and a spacelike configuration of fixed norm. The independent vector equation determines a local Lagrange multiplier and a temporal component that permits a regular ingoing extension across metric horizons. Reconstruction of the matter functions identifies a continuous family of wormholes, null minimum geometries, and black-bounces within one action. In the black hole case, the areal photon sphere and critical timelike orbit radii retain their Schwarzschild values, whereas angular deflection, periapsis advance, and photon orbit instability depend on the bounce and bumblebee parameters. The metric shadow coincides with the Schwarzschild prediction at fixed lapse mass and areal observer position; in addition, the adopted Sgr A* shadow diameter and M87* angular mass comparisons do not determine these parameters separately. The coupled axial equations yield distinct tensor, metric, and transverse bumblebee characteristics. We compute fundamental auxiliary massless scalar and ordinary Maxwell probe resonances by Chebyshev spectral collocation and estimate the tensor and bumblebee resonance scales at leading geometric optics order. Nonnegative probe potentials exclude exponentially growing probe modes. For negative nonminimal coupling and a nonzero temporal case, however, the supporting electromagnetic field develops an angular gradient instability in its extraordinary polarization. The unstable characteristic persists in the coupled principal symbol, while a variational construction establishes growing modes on the fixed geometry and lower bounds on their growth rates.