Black holes and their horizons in semiclassical and modified theories of gravity

Black holes are arguably the most celebrated prediction of general relativity (GR). Due to spectacular advances in observational astronomy, strong evidence for the existence of dark massive compact objects (so-called astrophysical black holes) has accumulated over the last few decades, thus gradually shifting our perception of black holes from purely mathematical curiosities to real physical entities. 

For distant observers black holes correspond to trapped spacetime domains bounded by apparent horizons. In this thesis, we present properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We derive their properties and present the implications. 

The formation of black holes follows a unique scenario involving both types of solutions. The solutions are real-valued only if the null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which is demonstrated in negative energy density firewalls. Close to the horizon, the energy-momentum tensor is uniquely identified up to a function of time and two pairs of signs. Using this result, we show that black hole evaporation and models of thin shell collapse do not have an independent physical meaning, but rather simply illustrate their underlying assumptions. The two principal generalisations of surface gravity to dynamic black hole spacetimes are discordant and do not match the semiclassical results. Neither of them can describe the emission of nearly-thermal radiation. If semiclassical gravity is valid, this implies that it is impossible to simultaneously realise all of the necessary elements (event horizon, evaporation, thermal character of the radiation) that would be required for a self-consistent formulation of the information loss paradox. Moreover, comparisons of the required energy and timescales with established semiclassical results suggest that the observed astrophysical black holes are horizonless ultra-compact objects, and the presence of a horizon would be indicative of new physics.

Modified theories of gravity must satisfy several constraints to be compatible with the dynamic black hole solutions of semiclassical gravity. We find that fourth-order gravity theories (generic modifications of the semiclassical Einstein equations including up to fourth-order derivatives of the metric) identically satisfy all of the necessary constraints and naturally accommodate both classes of semiclassical black hole solutions. Consequently, the semiclassical solutions can be regarded as zeroth-order terms in perturbative solutions of these models, and the observation of an apparent horizon by itself may not suffice to distinguish between the predictions of the semiclassical theory and those of higher-derivative gravity theories with up to fourth-order derivatives of the metric.