Analogue models of classical and semiclassical gravity

Abstract

Formal analogies between gravitational and acoustic or optical phenomena have been a subject of study for over a century, leading to interesting scenarios for testing kinematic aspects of general relativity in terrestrial laboratories. Here, some aspects about analog models of gravity obtained from the description of these two different kind of systems are analysed. First, light propagation in linear magnetoeletric media is examined. In particular, it is shown that this effect produces mixed time-space terms in the effective metric that depend only on the antisymmetric part of the generally non-symmetric magnetoelectric coefficient. Furthermore, the dispersion relation related to the linear effect motivates the analysis of an idealised exact model presenting an analog event horizon. Then, a short discussion comparing different ways of constructing analog models is provided. Subsequently, motivated by the results obtained in the optical context, we make a bibliographic review about those analog models obtained from moving media, establishing an equivalence between the propagation of acoustic perturbations in such a background and the propagation of free scalar fields near a Schwarschild black hole. This last aspect drives us to analyse the particle production in this scenario, a result that was first addressed by Stephen Hawking [1, 2], which yields to the the description of the so called Hawking radiation. When treating a non-stationary spacetime, particularly those presenting a gravitational collapse, we can extend the description of quantum fields to curved spacetimes by splitting the metric into two asymptotically stationary regions, with that we show that the presence of the horizon is fundamental for the creation of particles. Finally, it is also shown that the thermal distribution of this particle emission is identical to the Planck distribution for bosons, and because of that the Hawking temperature appears to be very small when we consider astrophysical scenarios.