An investigation of information loss in black hole spacetimes is performed. We demon- strate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the ra- diation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schr ̈dinger picture. o We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric space- time with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a self- similarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.

L'effet Hawking prédit, dans un espace-temps décrivant l'effondrement d'une étoile à symétrie sphérique vers un trou noir de Schwarzschild, qu'un observateur statique, situé à l'infini, observera un flux thermal de particules quantiques à la température de Hawking. La première démonstration mathématique de l'effet Hawking pour des champs quantiques libres est due à Bachelot, dont le travail sur les champs de Klein-Gordon a été ensuite étendu aux champs de Dirac, d'abord par Bachelot lui-même, puis par Melnyk. Ces travaux, placés dans le cadre d'une symétrie sphérique, ont été complétés par Häfner, qui donna une démonstration rigoureuse de l'effet Hawking pour des champs de Dirac, autour d'une étoile s'effondrant vers un trou noir de Kerr. Le but de cette thèse est d'étudier l'effet Hawking non plus dans un modèle de champs quantiques libres, où les problèmes posés se ramènent à l'étude d'équations aux dérivées partielles linéaires, mais dans un modèle de champs de Dirac en interaction. L'interaction est supposée à support compact, statique, et localisée à l'extérieur de l'étoile. Nous choisissons de traiter le cas d'un modèle jouet, dans un espace-temps de dimension 1+1, situation à laquelle on peut se ramener, au moins dans le cas libre, en utilisant la symétrie sphérique du problème. Nous étudions le comportement de champs de fermions de Dirac dans différentes situations : d'abord, pour une observable suivant l'effondrement de l'étoile ; puis pour une observable stationnaire ; enfin, pour une interaction dépendante du temps, localisée près de la surface de l'étoile. Dans chacun de ces cas, nous montrons l'existence de l'effet Hawking et donnons l'état limite correspondant.

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

This thesis is concerned with various methods for the control and investigation of pulse dynamics in a Photonic Crystal Fibre (PCF) and of the radiation driven by a short pulse. In particular the focus is on pulses in the anomalous dispersion region which would form solitons in the absence of higher order effects. Several different types of radiation can be driven by such pulses if they are perturbed by higher order dispersive and non-linear effects - for example Resonant Radiation (RR) and Negative Resonant Radiation (NRR) two dispersive waves which gain energy at the expense of the pulse. The feature of NRR which is of particular importance is that it is the first observed example of a coupling between positive and negative frequencies in optics. This has only been possible due to recent advances in fields such as PCFs, lasers and analogue systems. As with many scientific discoveries, NRR was found by bringing together ideas and techniques from these different fields. Both the pulse and the driven radiation are investigated using a number of different pulse and PCF parameters. These include power, chirp, polarisation and PCF dispersion. These are used to vary the wavelengths at which the driven radiation occurs as well as its generation efficiency. Furthermore the power and chirp are used to vary where in the PCF the driven radiation is generated by controlling where the driving pulse compresses and spectrally expands. This property is used to investigate different stages in the evolution of the pulse and driven radiation as well as to optimise the generation efficiency of the driven radiation.

<p>Penrose's inequality which relates the total mass of a space-time containing a black hole with the area of the event horizon, is a yet unproven condition that is required for the cosmic censorship hypothesis. It is believed that the inequality could be proved by using properties of the Hawking mass. This thesis gives analytical expressions for the Hawking mass in slowly rotating Kerr and Kerr-Newman space-times. It is also shown that the expressions are monotonically increasing, a result that does not contradict Penrose's inequality.</p>

Penrose's inequality which relates the total mass of a space-time containing a black hole with the area of the event horizon, is a yet unproven condition that is required for the cosmic censorship hypothesis. It is believed that the inequality could be proved by using properties of the Hawking mass. This thesis gives analytical expressions for the Hawking mass in slowly rotating Kerr and Kerr-Newman space-times. It is also shown that the expressions are monotonically increasing, a result that does not contradict Penrose's inequality.

As an operational approach to the Bekenstein-Hawking formula S_{BH}=A/4l_{Pl}^{2} for the black hole entropy, we consider the reversible contraction of a spinning thin shell to its event horizon and find that its thermodynamic entropy approaches $S_{\mathrm{BH}}$. In this sense the shell, called a "black shell", imitates and is externally indistinguishable from a black hole. Our work is a generalization of the previous result [10] for the spherical case. We assume the exterior space-time of the shell is given by the Kerr metric and match it to two different interior metrics, a vacuum one and a non-vacuum one. We find the vacuum interior embedding breaks down for fast spinning shells. The mechanism is not clear and worth further exploring. We also examine the case of a Kerr-AdS exterior, without trying to find a detailed interior solution. We expect the same behavior of the shell when the horizon limit is approached.

With the start of the age of the Large Hadron Collider (LHC) two challenges face theoreticians and computational physicists. The first is about understanding theories beyond the Standard Model and producing verifiable predictions that can be tested against what the LHC and subsequent machines would produce. The second is to improve computational methods so that the new experimental precision is matched by a theoretical one. But this improvement is also crucial for the detection of potential deviations from Standard Model predictions and possibly also finding the elusive Higgs. This work tries to address problems in both areas. In the first part we study the effects of adding tension in considering a black-hole on a brane. Such black-holes are predicted by some models as potential phenomena at the LHC. We calculate the effects of adding tension on observable quantities of black-holes, namely, quasinormal mode frequencies and Hawking radiation, and we show how this improves predictions. In the second part we investigate the computational problem of extending the Britto-Cachazo-Feng-Witten (BCFW) method to 1-loop level. The BCFW has been successfully used in recent years to compute scattering amplitudes at tree-level by suitably complex-shifting external momenta and reducing diagrams to simpler ones. In our investigation we establish that the BCFW can be extended to 1-loop, which means that 1-loop integrands can be treated as trees and can be broken down further into even simpler trees using the BCFW. We explicitly look at the effects of the shift for the lowest three n-point cases, but also demonstrate how the result extends to arbitrary n.

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.