Metric-affine Simpson–Visser field reconstruction and stability

Determine the corresponding field reconstruction for the Simpson–Visser geometry in metric-affine bumblebee gravity and characterize how nonmetricity influences the propagation and stability of the supporting fields.

Background

The paper constructs and analyzes a Simpson–Visser solution in metric bumblebee gravity using the Levi–Civita connection of the physical metric. It derives the supporting scalar, nonlinear electromagnetic, and fixed-norm bumblebee fields, and studies their propagation characteristics and instabilities within the metric formulation.

The authors identify the metric-affine extension as unresolved. In that formulation, the connection is varied independently and nonmetricity can modify both the reconstructed supporting fields and the characteristic structure governing their perturbations. Establishing the corresponding solution and determining the effects of nonmetricity on propagation and stability are therefore left as explicit problems.