Second Sound Horizon

We study an analogy between black hole physics and the phase boundary between normal and superfluid liquid helium in a gravitational field or in the presence of a constant heat current. We investigate the propagation of second sound near the boundary between superfluid and normal fluid. The speed of second sound should approach zero as it propagates toward the phase boundary where the reflection and transmission of the second sound will become ambiguous. This is analogous to the propagation of light near a singular black hole. When the phase boundary moves it is analogous to a black hole horizon: a second sound horizon. The analogy may lead us to infer a thermal radiation noise of amplitude <50 pico Kelvin from the boundary between the super and normal fluid. This thermal noise may be dramatize by applying a constant heat current from the bottom. We find a scaling behavior TQ^1/6 for the thermal radiation of the phase boundary as a function of heat current Q. A feasible experiment to measure this thermal noise is suggested.