Analogous Hawking Radiation in Dispersive Media

In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided.