Spectral properties for the Klein-Gordon Hamiltonian in charged black hole backgrounds

Charged massive scalar fields on charged black hole backgrounds are investigated through methods of spectral analysis in Krein spaces. We consider, on the three charged black hole backgrounds (Nariai, Reissner-Nordstrom, ultracold-II) taken into account, a necessary condition for the existence of complex eigenvalues. We show that even if it is satisfied, in two cases (Nariai and ultracold-II), by direct calculation, they actually cannot exist. In both cases, the Klein paradox occurs without restriction on the parameters. In the third case, the condition for their existence is shown to coincide with the condition, allowing the quantum discharge phenomenon associated with the Klein paradox. We also clarify the role of classical potentials, which appear in the physical literature on the subject, giving rise to the so-called level-crossing appearing in semiclassical calculations, and we comment on problems occurring in quantum field theory in the presence of complex eigenvalues.

Automated summary

Charged massive scalar fields on charged black hole backgrounds are studied using spectral analysis in Krein spaces. Necessary condition for the existence of complex eigenvalues is considered on three charged black hole backgrounds (Nariai, Reissner-Nordstrom, ultra cold-II). It is shown that in two cases (Nariai and ultracold-II), even if the condition is satisfied, complex eigenvalues do not actually exist. Klein paradox occurs without restriction on the parameters in both cases. In the third case, the condition for existence of complex eigenvalues coincides with the condition for quantum discharge phenomenon associated with the Klein paradox. The role of classical potentials, appearing in the physical literature, is clarified and problems in quantum field theory with complex eigenvalues are discussed.