Thermal quasi-equilibrium states across Landau horizons in the effective gravity of superfluids

We give an account of the physical behaviour of a quasiparticle horizon due to non-Lorentz invariant modifications of the effective spacetime experien ced by the quasiparticles ("matter") for high momenta. By introducing a "re lativistic" conserved energy-momentum tenser, we derive quasi-equilibrium s tates of the fluid across the "Landau" quasiparticle horizon at temperature s well above the quantum Hawking temperature. Nonlinear dispersion of the q uasiparticle energy spectrum is instrumental for quasiparticle communicatio n and exchange across the horizon. It is responsible for the establishment of the local thermal equilibrium across the horizon with the Tolman tempera ture being inhomogeneous behind the horizon. The inhomogeneity causes relax ation of the quasi-equilibrium states due to scattering of thermal quasipar ticles, which finally leads to a shrinking black hole horizon. This process serves as the classical thermal counterpart of the quantum effect of Hawki ng radiation and will allow for an observation of the properties of the hor izon at temperatures well above the Hawking temperature. We discuss the the rmal entropy related to the horizon. We find that only the first nonlinear correction to the energy spectrum is important for the thermal properties o f the horizon. They are fully determined by an energy of order E-Planck(T/E -Planck)(1/3), which is well below the Planck energy scale EPlanck, SO that Planck scale physics is not involved in determining thermal quantities rel ated to the horizon.