Title:

Hawking radiation in dispersive media

Hawking radiation, despite its presence in theoretical physics for over thirty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from conceptual difficulties. Of particular note is the transPlanckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to systems which model the spacetime geometry of black holes, and which, by analogy, are also thought to emit Hawking radiation. These analogue systems typically exhibit dispersion, which regularizes the wave behaviour at the horizon but does not lend itself well to analytic treatment, thus rendering Hawking’s prediction less secure. A general analytic method for dealing with Hawking radiation in dispersive systems has proved difficult to find. This thesis presents new numerical and analytic results for Hawking emission spectra in dispersive systems. It examines two blackhole analogue systems: it begins by introducing the wellknown acoustic model, presenting some original results in that context; then, through analogy with the acoustic model, goes on to develop the lesserknown fibreoptical model. The following original results are presented in the context of both of these models: • an analytic expression for the lowfrequency temperature is found for a hyperbolic tangent background profile, valid in the entire parameter space; it is wellknown that the spectrum is approximately thermal at low frequencies, but a universally valid expression for the corresponding temperature is an original development; • an analytic expression for the spectrum, valid over almost the entire frequency range, when the velocity profile parameters lie in the regime where the lowfrequency temperature is given by the Hawking prediction; previous work has focused on the lowfrequency thermal spectrum and the characterization of the deviations from thermality, rather than a single analytic expression; and • a new unexplored regime where no groupvelocity horizon exists is examined; the Hawking spectra are found to be nonzero here, but also highly nonthermal, and are found, in the limit of small deviations, to vary with the square of the maximum deviation; the analytic expression for the case with a horizon is found to carry over to this new regime, with appropriate modifications. Furthermore, the thesis examines the results of a classical frequencyshifting experiment in the context of fibreoptical horizons. The theory of this process is presented for both a constantvelocity and a constantlydecelerating pulse, the latter case taking account of the Raman effect. The resulting spectra are at least qualititively explained, but there is a discrepancy between theory and experiment that has not yet been accounted for.
