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We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact solution for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a 1+1-dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal. The scattering coefficients were previously obtained by Busch and Parentani in a study of dispersive fields in de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further details of the wave propagation in this exactly solvable case, where our focus is on laboratory systems.
In the context of analog gravity the Hawking effect can be generalized to domains outside astrophysics. Arguably, the most successful systems for this analogy have been so far the sonic and the optical ones. However, problems arise in the analog syst
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two values $r_{1
We present a simple exact solution for the interior of a rotating star. The interpretation of the stress energy tensor as that of a fluid requires the existence of a high viscosity, which is quite expected for a rotating fluid. In spite of the negati
Observing quantum particle creation by black holes (Hawking radiation) in the astrophysical context is, in ordinary situations, hopeless. Nevertheless the Hawking effect, which depends only on kinematical properties of wave propagation in the presenc
We consider further on the problem of the analogue Hawking radiation. We propose a fourth order ordinary differential equation, which allows to discuss the problem of Hawking radiation in analogue gravity in a unified way, encompassing fluids and die