Figure 15

Figure 15: The picture shows a subsonic dispersion relation as a relation ω − vk = ±c |k|Γ k. In particular we plot a dispersion of the type ∘ -------2---2- Γ k = K tanh (k ∕K ) originally employed by Unruh. For supersonic velocities the dispersion relation has two real roots. For subsonic velocities and ω greater than a critical frequency ωc, the dispersion relation has four real roots.