General restrictions on nonstationary signature-changing scalar transitions

Investigate whether nonstationary scalar transitions obey general restrictions or no-go results in modified-gravity models admitting Euclidean–Lorentzian signature change.

Background

The paper constructs a critical exponential-potential branch in scalar–tensor gravity in which the Einstein-frame scalar is generically nonstationary at the signature-changing hypersurface. Unlike the stationary oscillator branch, this case requires a coupling-dependent condition for vanishing Jordan-frame extrinsic curvature and may require an additional smoothness analysis after transforming to the degenerate transverse coordinate.

The authors identify this behavior as suggesting a broader unresolved question: whether nonstationary scalar transitions are subject to general restrictions or no-go theorems across modified-gravity theories that permit Euclidean–Lorentzian signature change.