Abstract:The Hawking flux from a black hole, (at least as seen from asymptotic infinity), is extremely sparse and thin, with the average time between emission of the successive Hawking quanta being many times larger than the natural timescale set by the energies of the emitted quanta. While this result has been known for over 30 years, it has largely been forgotten, possibly because many subsequent authors focussed mainly on the late-time high-temperature regime. We shall instead focus on the early-stage lowtemperature regime, and shall both quantify and significantly extend these observations in a number of different ways. In particular we shall confront numerical estimates with semi-analytic approximations based on a naive Planck spectrum.First we shall identify several natural dimensionless figures of merit, and thereby compare the mean time between emission of successive Hawking quanta to several distinct but quite natural timescales that can be associated with the emitted quanta, demonstrating that very large ratios are typical for emission of massless quanta from a Schwarzschild black hole. Furthermore these ratios are independent of the mass of the black hole as it slowly evolves. We shall then show that the situation for the more general Reissner-Nordström and generic "dirty" black holes is even worse, at least as long as the surrounding matter satisfies some suitable energy conditions. The situation for the Kerr and Kerr-Newman black holes (or even for charged particle emission from a Reissner-Nordström black hole) is considerably trickier, and depends on a careful accounting of the super-radiant modes.Overall, the Hawking quanta are seen to be dribbling out of the black hole one at a time, in an extremely slow cascade of 2-body decays. Among other things, this implies that the Hawking flux is subject to "shot noise". Observationally, the Planck spectrum of the Hawking flux can only be determined by collecting and integrating data over a very long timescale. We conclude by connecting these points back to various kinematic aspects of the Hawking evaporation process.

Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-)material would provide an analogue space-time model or -vice versa -characterizing which given metric could be modelled with a (meta-)material. While the consistency conditions themselves are by now well known and studied, the form the metric takes once they are satisfied is not. This question is mostly easily answered by keeping the formalisms of the two research fields here in contact as close to each other as possible. While fully covariant formulations of the electrodynamics of media have been around for a long while, they are usually abandoned for (3+1)-or 6-dimensional formalisms. Here we shall use the fully unified and fully covariant approach. This enables us even to generalize the consistency conditions for the existence of an effective metric to arbitrary background metrics beyond flat space-time electrodynamics. We also show how the familiar matrices for permittivity ǫ, permeability µ −1 , and magneto-electric effects ζ can be seen as the three independent pieces of the Bel decomposition for the constitutive tensor Z abcd , i.e., the components of an orthogonal decomposition with respect to a given observer with four-velocity V a . Finally, we shall use the Moore-Penrose pseudo-inverse and the closely related pseudo-determinant to then gain the desired reconstruction of the effective metric in terms of the permittivity tensor ǫ ab , the permeability tensor µ −1 ab , and the magneto-electric tensor ζ ab , as an explicit function g eff (ǫ, µ −1 , ζ).

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With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes.

Modern meta-materials allow one to construct electromagnetic media with almost arbitrary bespoke permittivity, permeability, and magneto-electric tensors. If (and only if) the permittivity, permeability, and magneto-electric tensors satisfy certain stringent compatibility conditions, can the meta-material be fully described (at the wave optics level) in terms of an effective Lorentzian metric -an analogue spacetime. We shall consider some of the standard black-hole spacetimes of primary interest in general relativity, in various coordinate systems, and determine the equivalent meta-material susceptibility tensors in a laboratory setting. In static black hole spacetimes (Schwarzschild and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the horizon. In stationary black hole spacetimes (Kerr and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the ergo-surface.