Integral method for the calculation of Hawking radiation in dispersive media II. Asymmetric asymptotics

Analogue gravity experiments make feasible the realisation of black hole spacetimes in a laboratory setting and the observational verification of Hawking radiation. Since such analogue systems are typically dominated by dispersion, efficient techniques for calculating the predicted Hawking spectrum in the presence of strong dispersion are required. In the preceding paper, an integral method in Fourier space is proposed for stationary $1+1$-dimensional backgrounds which are asymptotically symmetric. Here, this method is generalised to backgrounds which are different in the asymptotic regions to the left and right of the scattering region.