Observation of a phase space horizon with surface gravity water waves

In 1974, Stephen Hawking predicted that quantum effects in the proximity of a black hole lead to the emission of particles and black hole evaporation. At the very heart of this process lies a logarithmic phase singularity which leads to the Bose-Einstein statistics of Hawking radiation. An identical singularity appears in the elementary quantum system of the inverted harmonic oscillator. In this Letter we report the observation of the onset of this logarithmic phase singularity emerging at a horizon in phase space and giving rise to a Fermi-Dirac distribution. For this purpose, we utilize surface gravity water waves and freely propagate an appropriately tailored energy wave function of the inverted harmonic oscillator to reveal the phase space horizon and the intrinsic singularities. Due to the presence of an amplitude singularity in this system, the analogous quantities display a Fermi-Dirac rather than a Bose-Einstein distribution. Since 1974, it was theoretically postulated that black holes, despite their name, emit radiation with a spectrum like that of a black body. Utilizing surface gravity water waves to emulate black hole physics, the authors reveal the emergence of a logarithmic phase singularity analogous to that predicted by Hawking in black holes, whose energy distribution associated with the singularity results in a Fermi-Dirac distribution instead of the familiar Bose-Einstein statistics of the Hawking radiation.