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Register a new userHawking temperature in dispersive media: Analytical and numerical study
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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 systems as their dispersive effects are too large to be ignored, and this in turn modifies the usual thermal spectrum of Hawking radiation. In this work we perform analytical and numerical studies on how the velocity profile modifies the Hawking temperature in dispersive media, including some with direct experimental application.
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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.
Acoustic holes are the hydrodynamic analogue of standard black holes. Featuring an acoustic horizon, these systems spontaneously emit phonons at the Hawking temperature. We derive the Hawking temperature of the acoustic horizon by fully exploiting the analogy between black and acoustic holes within a covariant kinetic theory approach. After deriving the phonon distribution function from the covariant kinetic equations, we reproduce the expression of the Hawking temperature by equating the entropy and energy losses of the acoustic hole and the entropy and energy gains of the spontaneously emitted phonons. Differently from previous calculations we do not need a microscopical treatment of normal modes propagation. Our approach opens a different perspective on the meaning of Hawking temperature and its connection with entropy which may allow an easier study of non stationary horizons beyond thermodynamic equilibrium.
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 presence of horizons, is present also in nongravitational contexts, for instance in stationary fluids undergoing supersonic flow. We present results on how to observe the analog Hawking radiation in Bose-Einstein condensates by a direct measurement of the density correlations due to the phonon pairs (Hawking quanta-partner) created by the acoustic horizon.
We find necessary and sufficient conditions for existence of a locally isometric embedding of a vacuum space-time into a conformally-flat 5-space. We explicitly construct such embeddings for any spherically symmetric Lorentzian metric in $3+1$ dimensions as a hypersurface in $R^{4, 1}$. For the Schwarzschild metric the embedding is global, and extends through the horizon all the way to the $r=0$ singularity. We discuss the asymptotic properties of the embedding in the context of Penroses theorem on Schwarzschild causality. We finally show that the Hawking temperature of the Schwarzschild metric agrees with the Unruh temperature measured by an observer moving along hyperbolae in $R^{4, 1}$.
As distinct from the black hole physics, the de Sitter thermodynamics is not determined by the cosmological horizon, the effective temperature differs from the Hawking temperature. In particular, the atom in the de Sitter universe experiences thermal activation corresponding to the local temperature, which is twice larger than the Hawking temperature, $T_{rm loc}=2T_{rm Hawking}$. The same double Hawking temperature describes the decay of massive scalar field in the de Sitter universe. The reason, why the local temperature is exactly twice the Hawking temperature, follows from the geometry of the de Sitter spacetime. The weakening of the role of the cosmological horizon in de Sitter universe is confirmed by considering Hawking radiation. We discuss the difference between the radiation of particles in the de Sitter spacetime and the Schwinger pair creation in the electric field. We use the stationary Painleve-Gullstrand metric for the de Sitter spacetime, where the particles are created by Hawking radiation from the cosmological horizon, and time independent gauge for the electric field. In these stationary frames the Hamiltonians and the energy spectra of massive particles look rather similar. However, the final results are essentially different. In case of Schwinger pair production the number density of the created pairs grows with time, while in the de Sitter vacuum the number density of the created pairs is finite. The latter suggests that Hawking radiation from the cosmological horizon does not lead to instability of the de Sitter vacuum. The other mechanisms of instability are required for the dynamical solution of the cosmological constant problem. We consider the possible role of the local temperature $T_{rm loc}=2T_{rm H}$ in the decay of the de Sitter space-time due to the energy exchange between the vacuum energy and relativistic matter with this temperature.
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