The effects of strong gravity on the dispersion relation of massive particles in the Kaluza-Klein theory

We derive a modified dispersion relation for massive particles within the frameworks of five-dimensional Kaluza-Klein theory and general relativity, taking into account strong gravitational effects. The resulting effective mass depends on the curvature of the underlying phase space. Notably, in regions with strong gravitational fields, the effective mass may become imaginary, implying the possibility of particle decay induced by spacetime curvature.