The core of this thesis is the analysis of accelerating black hole solution with the NUT parameter, which was found by Chng, Mann and Stelea in 2006, and related spacetimes. The original work consists of three interconnected parts. In the first chapter we study the Taub-NUT solution, in particular the nature of its pathological axes, and we include a number of visualizations. In the second chapter we investigate the accelerating Taub-NUT solution, we present it in a new form, and we discuss its "deviation" from the Pleba'nski-Demia'nski class of solutions. To see the differences more clearly, in the final chapter we put also the Pleba'nski-Demia'nski metric into a completely new factorized form. The work is concluded by discussion of special subcases, from which it is clearly seen that the Pleba'nski-Demia'nski class does not contain the accelerating Taub-NUT solution.

The semi-classical black hole tunnelling method is a useful technique to calculate black hole temperature and understand black hole thermodynamics. I will investigate the black hole tunnelling method in detail. I will compare two different approaches used to calculate black hole tunnelling. The tunnelling method can be applied to a broad range of spacetimes and I will show this explicitly in order to demonstrate the robustness of the tunnelling technique. In particular, I will apply the tunnelling method to spacetimes including: Rindler (the method can recover the Unruh temperature), and more general spacetimes (such as Kerr-Newman and Taub-NUT). I will also discuss the 5d Kerr-Gödel spacetimes in detail (while showing a previous unobserved property of these spaces). Once the parameter space of Kerr-Gödel is understood in detail, I will show how the tunnelling method can also be successfully applied to the Kerr-Gödel black hole. Finally, the key result of my thesis involves extending the tunnelling method to model fermion emission. The previous tunnelling calculations all involved the emission of scalar particles. I will model the emission of spin-1/2 fermions from various spacetimes including the Rindler spacetime and general non-rotating black holes. I will also model the emission of charged spin-1/2 fermions from the Kerr-Newman spacetime to show that the method is also applicable to rotating spacetimes. In all these cases I show that the correct Hawking temperature (Unruh temperature in the case of Rindler) is recovered for spin-1/2 fermion emission. Although this final result is not surprising, it is an important result because it confirms that Dirac particles will radiate from the black hole at the same temperature as scalar particles. It has always been assumed that this is the case but there is very little literature involving fermion radiation of black holes. So the results of my calculations are twofold, I demonstrate that Dirac particles are emitted at the same temperature as scalar particles from a black hole and it shows how robust the semi-classical tunnelling technique is.

The semi-classical black hole tunnelling method is a useful technique to calculate black hole temperature and understand black hole thermodynamics. I will investigate the black hole tunnelling method in detail. I will compare two different approaches used to calculate black hole tunnelling. The tunnelling method can be applied to a broad range of spacetimes and I will show this explicitly in order to demonstrate the robustness of the tunnelling technique. In particular, I will apply the tunnelling method to spacetimes including: Rindler (the method can recover the Unruh temperature), and more general spacetimes (such as Kerr-Newman and Taub-NUT). I will also discuss the 5d Kerr-Gödel spacetimes in detail (while showing a previous unobserved property of these spaces). Once the parameter space of Kerr-Gödel is understood in detail, I will show how the tunnelling method can also be successfully applied to the Kerr-Gödel black hole. Finally, the key result of my thesis involves extending the tunnelling method to model fermion emission. The previous tunnelling calculations all involved the emission of scalar particles. I will model the emission of spin-1/2 fermions from various spacetimes including the Rindler spacetime and general non-rotating black holes. I will also model the emission of charged spin-1/2 fermions from the Kerr-Newman spacetime to show that the method is also applicable to rotating spacetimes. In all these cases I show that the correct Hawking temperature (Unruh temperature in the case of Rindler) is recovered for spin-1/2 fermion emission. Although this final result is not surprising, it is an important result because it confirms that Dirac particles will radiate from the black hole at the same temperature as scalar particles. It has always been assumed that this is the case but there is very little literature involving fermion radiation of black holes. So the results of my calculations are twofold, I demonstrate that Dirac particles are emitted at the same temperature as scalar particles from a black hole and it shows how robust the semi-classical tunnelling technique is.

La solution des équations d'Einstein–Maxwell décrivant le trou noir le plus général a été découverte par Plebański et Demiański en 1976. Cette thèse accomplit plusieurs étapes en vue d'intégrer une généralisation de cette solution en supergravité jaugée N = 2. Le contenu bosonique de cette dernière comprend la métrique assortie de champs de jauge et de deux types de champs scalaires (appelés scalaires-vecteurs et hyperscalaires); cela implique qu'il est beaucoup plus compliqué de trouver une solution générale et l'on doit se restreindre à des classes particulières de solutions ou bien utiliser des algorithmes pour générer des solutions.Dans la première partie de cette thèse nous approchons ce problème grâce à la première stratégie en nous restreignant aux solutions BPS.Dans un premier temps nous étudions les jaugeages abéliens qui impliquent les hyperscalaires afin de comprendre quelles sont les conditions nécessaires pour obtenir des vides N = 2 adS4 ainsi que des géométries de proche-horizon associées à des trous noirs statiques.Par la suite nous décrivons une solution générale et analytique pour des trous noirs (extrémaux) 1/4-BPS qui possèdent une masse, une charge de NUT, des charges dyoniques et des champs scalaires non-triviaux dans le contexte de la supergravité N = 2 jaugée à la Fayet–Iliopoulos.Dans la seconde partie nous obtenons une extension de l'algorithme de Janis-Newman afin de prendre en compte tous les champs bosoniques de spin inférieur à 2, les horizons topologiques et le cas des autres dimensions.Ainsi cela met à disposition tous les outils nécessaires pour appliquer cet algorithme à la supergravité (jaugée ou non). / The most general black hole solution of Einstein–Maxwell theory has been discovered by Plebański and Demiański in 1976.This thesis provides several steps towards generalizing this solution by embedding it into N = 2 gauged supergravity.The (bosonic fields of the) latter consists in the metric together with gauge fields and two kinds of scalar fields (vector scalars and hyperscalars); as a consequence finding a general solution is involved and one needs to focus on specific subclasses of solutions or to rely on solution generating algorithms. In the first part of the thesis we approach the problem using the first strategy: we restrict our attention to BPS solutions, relying on a symplectic covariant formalism. First we study the possible Abelian gaugings involving the hyperscalars in order to understand which are the necessary conditions for obtaining N = 2 adS4 vacua and near-horizon geometries associated to the asymptotics of static black holes.A preliminary step is to obtain covariant expressions for the Killing vectors of symmetric special quaternionic-Kähler manifolds. Then we describe a general analytic solutions for 1/4-BPS (extremal) black holes with mass, NUT, dyonic charges and running scalars in N = 2 Fayet–Iliopoulos gauged supergravity with a symmetric very special Kähler manifold. In the second part we provide an extension of the Janis–Newman algorithm to all bosonic fields with spin less than 2, to topological horizons and to other dimensions. This provides all the necessary tools for applying this solution generating algorithm to (un)gauged supergravity, and interesting connections with the N = 2 supergravity theory are unravelled.

L'algorithme covariant de van Holten, servant à construire des quantités conservées, est présenté avec une attention particulière portée sur les vecteurs de type Runge-Lenz. La dynamique classique des particules portant des charges isospins est passée en revue. Plusieures applications physiques sont considerées. Des champs de type monopôles non-Abéliens, générés par des mouvements nucléaires dans les molécules diatomiques, introduites par Moody, Shapere et Wilczek, sont étudiées. Dans le cas des espaces courbes, le formalisme de van Holten permet de décrire la symétrie dynamique des monopôles Kaluza-Klein généralisés. La procédure est étendue à la supersymétrie et appliquée aux monopôles supersymétriques. Une autre application, concernant l'oscillateur non-commutatif en dimension trois, est également traitée.