Determine the fully dynamical geodesic behavior and observable signatures

Determine the fully dynamical motion of particles and photons in the regularized McVittie spacetime beyond the quasi-static approximation, including whether the regular core and cosmological regularization produce observable effects in gravitational lensing, photon-ring or shadow formation, and matter or radiation propagation.

Background

The paper studies photon spheres, Lyapunov exponents, and innermost stable circular orbits by treating the cosmological scale factor as approximately constant over an orbital period. This quasi-static treatment does not capture the complete time-dependent geodesic dynamics of the regularized McVittie geometry.

The unresolved problem is to replace that approximation with a fully dynamical analysis and establish whether the two regularization mechanisms leave measurable imprints on optical and dynamical observables, including lensing, photon rings, shadows, and the propagation of matter and radiation.

References

A fully dynamical treatment of particle and photon motion beyond the quasi-static approximation would also be desirable. Such an analysis could clarify whether the regular core and the cosmological regularization leave observable imprints in lensing, photon-ring or shadow formation, or in the propagation of matter and radiation.

— On The Regularized McVittie Black Bounce and a Family of Traversable Wormholes  (2609.09238 - Chakrabarti et al., 8 Sep 2026) in Section Conclusion

Furthermore, the perturbative stability of the regularized spacetime and its response to scalar, electromagnetic, and gravitational perturbations remain important directions for future work. Such analyses could clarify whether the regularization of both the central compact object and the cosmological background leads to distinctive observable signatures.

— On The Regularized McVittie Black Bounce and a Family of Traversable Wormholes  (2609.09238 - Chakrabarti et al., 8 Sep 2026) in Section Conclusion