Black Hole Evaporation: Sparsity in Analogue and General Relativistic Space-Times

Our understanding of black holes changed drastically, when Stephen Hawking discovered their evaporation due to quantum mechanical processes. One core feature of this effect is both its similarity and simultaneous dissimilarity to classical black body radiation: A black holes spectrum certainly looks like that of a black/grey body, yet the number of emitted particles per unit time differs greatly. However it is precisely this emission rate that determines whether the resulting radiation field behaves classically or non-classically. It has been known nearly since the effects discovery that a black holes radiation is in this sense non-classical. However, this has been an utterly underappreciated property. In order to give a more readily quantifiable picture of this, we introduced the easily evaluated and interpreted notion of sparsity. Sadly, and much to relativists chagrin, astrophysical black holes (and their evaporation) tend to be observationally elusive entities. Luckily, Hawkings derivation lends itself to reformulations that survive outside its astrophysical origin - only three things are needed: a universal speed limit, a notion of a horizon, and lastly a sprinkle of quantum dynamics on top. With these ingredients at hand, the last thirty-odd years have seen a lot of work to transfer Hawking radiation into the laboratory, using a range of physical models. A large part of this thesis is aimed at providing electromagnetic analogues to prepare an analysis of our notion of sparsity in these analogues. For this, we developed extensively a purely algebraic/kinematical analogy based on covariant meta-material electrodynamics, but also an analytic/dynamical analogy based on stratified refractive indices. After introducing these analogue space-time models, we explain why the notion of sparsity is much more subtle and difficult to come by than in the original, astrophysical setting.