Event horizons in water flow: the math!
March 15, 2008In a previous post, I discussed recent research which demonstrated the creation of an artificial ‘event horizon’ in a fiber optic cable. In that post, I described how a river speeding up as it goes towards a waterfall has an event horizon: waves that are created past the horizon have no possibility of escape. This was illustrated by the figure below:

As you can see, I’ve drawn the wavefronts created by rocks dropped in the water as ellipses, which seems like the obvious solution: waves will be ’stretched out’ along the flow of the river, while they will spread normally perpendicular to the flow. Being a nitpicky sort of guy, though, I wanted to demonstrate that this is the case mathematically, which I do below the fold… (warning: algebra and calculus follow!)