Resumo:
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.
