Thin cylindrical shells in general relativity

Notes on static cylindrical shells

“…Langer [13], using Israel's formalism, worked out the case of a cylinder composed of two streams of free particles counter-orbiting in ±Φ-directions; and he found agreement of his results with those of Raychaudhuri and Som [14] who did not use the Israel formalism but a limiting procedure starting from a shell of a finite thickness. It turns out that in this case the parameter m + ∈ [0, 1).…”

Ultrafast studies of electron dynamics at metal-dielectric interfaces

“…These are wavefunctions that vanish at -cm, are standing waves normalized to 1 in the well, and give an exponentially small probability current at positive q. The nonconservation of probability current requires that the energy of the metastable level have an (exponentially small) imaginary part, as demonstrated long ago by Langer [162,163]. In his discussion, he showed that the partition function of a metastable system can be rigorously defined only as an analytic continuation in the parameter space from the region where the system is stable and well defined to the region where the system is metastable.…”